IMAGE  EVALUATION 
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Lorporation 


33  WEST  MAIN  STREET 

WEBSTER,  N.Y.  14580 

(716)  P72-4503 


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CIHM 
Microfiche 
Series 
([\/lonograplis) 


ICMH 

Collection  de 
microfiches 
(monographies) 


Canadian  Institute  for  Historical  Microreproductions  /  Institut  Canadian  de  microreproductions  historiquM 


-I  An 


Technical  and  Bibliographic  Notes  /  Notes  techniques  et  bibliographiques 


The  Institute  has  attempted  to  obtain  the  best  original 
copy  available  for  filming.   Features  of  this  copy  which 
may  be  bibliographically  unique,  which  may  alter  any 
of  the  images  in  the  reproduction,  or  which  irjy 
significantly  change  the  usual  method  of  filming,  are 
checked  below. 


j     TI  Coloured  covers/ 


n 


Couverture  de  couleur 

Covers  damaged/ 
Couverture  endommag^ 

Covers  restored  and/or  laminated/ 
Couverture  restauree  et/ou  pellicul6e 


□  Cover  title  missing/ 
Le  titre  de  couvertu 


couverture  manque 


j        I  Coloured  maps/ 


Caites  geographiques  en  couleur 

Coloured  ink  (i.-.  other  than  blue  or  black)/ 
Encre  de  couleur  (i.e.  autre  que  bleue  ou  noire) 

Coloured  plates  and/or  illustrations/ 
Planches  et/ou  illustrations  en  couleur 

Bound  with  other  material/ 
Relie  avec  d'autres  documents 

Tight  binding  may  c?"jse  shadows  or  distortion 
along  interior  margin/ 
La  leliure  serree  peut  causer  de  I'ombre  ou  de  la 
distorsion  le  long  de  la  marge  interieure 

Blank  leaves  added  during  restoration  may  appear 
within  the  text.  Whenever  possible,  these  have 
been  omitted  from  filming/ 
II  se  peut  que  certaines  pages  blanches  ajout^es 
lors  d'une  restauration  apparaissent  dans  le  texte, 
mais,  lorsque  cela  etait  possible,  ces  pages  n'ont 
pas  ete  filmees. 


□  Additional  comments:/ 
Commentaires  supplementaires: 

Thi.  (    m  is  filmed  at  the  reduction  ratio  checked  below/ 

Ce  document  est  filme  au  taux  de  reduction  indique  ci  dessous. 

^°^  14X  18X 


n 


n 


L'Institut  a  microfilm^  le  meilleur  exemplaire  qu'il 
lui  a  ete  possible  de  se  procurer.   Les  details  de  cet 
exemplaire  qui  sont  peut-«tre  uniques  du  point  de  vue 
bibliographique,  qui  peuvent  modifier  une  imcge 
reproduite,  ou  qui  peuvent  exiger  une  modification 
dai  s  la  methode  normale  de  filmage  sont  indiques 
ci-dessous. 

C~|  Coloured  pages/ 
J  Pagfcs  de  couleur 

□  Pages  damaged/ 
Pages  endommagees 

□  Pages  restored  and/or  laminated/ 
Pages  restaurees  et/ou  pellicultes 

0  Pages  discoloured,  stained  or  foxed/ 
Pages  decolorees,  tachetees  ou  piquees 

□  Pages  detached/ 
Pages  detachees 

r~~7|  Showth  rough/ 
■        I  Transparence 

I        I  Quality  of  print  varies/ 


Qualite  inegale  de  I'impression 

Continuous  paginati( 
Pagination  continue 


□  Continuous  pagination/ 
Pagination  continue 

0  Includes  index(es)/ 
Comprend  un  (des)  i 


ndex 


Title  on  header  taken  from:  / 
Le  titre  de  l'en-t£te  provient: 


□  Title  page  of  issue/ 
Page  de  titre  de  la  li 


vraison 


issue/ 
depart  de  la  livraison 


□  Caption  of 
Titre  de  de( 

Masthead/ 

Generique  (periodiques)  de  la  livraison 


I        I  Masthead/ 


23  X 


26  X 


30X 


y 


12X 


16X 


20X 


24  X 


28  X 


D 


22X 


'  / 


The  copy  filmed  here  has  been  reproduced  thanks 
to  the  generosity  of: 

National  Library  of  Canada 


L'exemplaire  film6  fut  reproduit  grace  d  la 
g6n6rosit6  de: 

Bibliothdque  nationale  du  C^iada 


The  images  appearing  here  are  the  best  quality 
possible  considering  the  condition  and  legibility 
of  the  original  copy  and  in  keeping  with  the 
filming  contract  specifications. 


Original  copies  m  printed  paper  covers  are  filmed 
beginning  with  rhe  front  cover  and  ending  on 
the  last  page  with  a  printed  or  illustrated  impres- 
sion, or  the  back  cover  when  appropriate.  All 
other  original  copies  are  filmed  beginning  on  the 
first  page  with  a  prjr.ted  or  illustrated  impres- 
sion, and  ending  on  tha  last  page  with  a  printod 
or  illustrated  impression. 


The  last  recorded  frame  on  each  microfiche 
shall  contain  the  symbol  -^  (meaning  "CON- 
TINUED"), or  the  symbol  V  (meaning  "END"), 
whichevar  applies. 

Maps,  plates,  charts,  etc.,  may  be  filmed  at 
different  reduction  ratios.  Those  too  large  to  be 
entirely  included  in  one  exposure  are  filmed 
beginning  in  the  upper  left  hand  corner,  left  to 
right  and  top  to  bottom,  as  many  frames  as 
required.  The  following  diagrams  illustrate  the 
method: 


Les  images  suivantes  ont  6t6  reproduites  avec  le 
plus  grand  soin,  compte  tenu  de  la  condition  et 
de  la  nettet6  de  l'exemplaire  filmd,  et  en 
conformit6  avec  les  conditions  du  contrat  de 
filmage. 

Les  exemplaires  originaux  dont  la  couverture  en 
papier  est  imprimde  sont  film6s  en  commengant 
par  le  premier  plat  et  en  terminant  soit  par  la 
dernidre  page  qui  ccinporte  une  empreinte 
d'impression  ou  d'illustration,  soit  par  le  second 
plat,  selon  le  cas.  Tous  les  autres  exemplaires 
ongiriaux  sont  film6s  en  commengant  par  la 
premidre  page  qui  comporte  une  empreinte 
d'impression  ou  d'illustration  et  en  terminant  par 
la  dernidre  page  qui  comporte  une  telle 
empreinte. 

Un  des  symboles  suivants  apparaitra  sur  la 
dernidre  image  de  cheque  microfiche,  selon  le 
cas:  le  symbole  — ^  signifie  "A  SUIVRE"   le 
symbole  V  signifie  "FIN". 

Les  cartes,  planches,  tableaux,  etc.,  peuvent  §tre 
film6s  d  des  taux  de  r6duction  diff6rents. 
Lorsque  le  document  est  trop  grand  pour  dtre 
'eproduit  en  un  seul  clich6,  il  est  film6  d  partir 
de  I'angle  sun6rieur  gauche,  de  gauche  d  droite, 
et  de  haut  en  bas,  en  prenant  le  nombre 
d'images  n6cessaire.  Les  diagrammes  suivants 
illustrent  la  mdthode. 


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ufntionnl  device. 


THE 


HJGH  SCHOOL  PHYSICS. 


BY 


ALFRKJ)    ]..   (iAUK,    M.A., 

moil   HCV    ..(,,    liOSTON,    MASS., 


AND 


C.  FESSENDEN,  M.A., 

moil   BCHOOr,,    NAPANKR,   OXT. 


A  u>homea  6,  ^„n-.^.  of  EaucaH„.f.>r  use  in  t„e  Schools  of  Ontario 

A  .nor,.,,  ,,,  0...a  .fr,.Uic  In.ru.io.for  „.  ,„  .,.,  LoU  ,  f  A..,  S..i. 

'  :;: : T"'1  " """'  ^— ^->'- --  ^^  a.  .e....  ,;.....;!ir- 

^»./,nn^<.,/  6,  Cou„e,l  of  P„Uic  In.M.tionf„r  u.e  in  the  School,  of  Q^elee 


I'RICP;, 


•Sl.OO. 


^v.  .J.  (;agi<:  x-  company, 

NEW   VOKK,    U.  s.  I 


TORONTO,    CAN, 


'J 


Kntered  according  to  Act  of  Parliament  o<  Canada.  In  the  Office  of  the  Minister  of 
Agriculture,  by  W.  J.  Oaob  &  Co..  in  the  year  one  thousand  eight  hundred  and 
•ighty-seven. 


hrj\- 


PREFACE  TO   THE   FOFRTH   EDITION 

— OF — 

HIGH    SCHOOL    PHYSICS. 


rpHE  American  Association  for  the  Advancement  of  Science   at  its 
-L      meetmg  in  1879,  appointed  a  committee  to  consider  the  subject 
of      Science-Teaching  in   the   Public  Schools."     The  followin.r  are 
extracts  from  the  report  of  this  committee  :— 

' '  T'^"- oug'l  books  and  teachers  the  pupil  is  filled  up  with  information  with 
regard  to  Science      Its  facts  and  principles  are  explained  as  far™   possUde 
and  then  left  in  the  memory  with  his  other  school  acquisitions!    HeTea  „: 
the  Sciences  much  as  he  learns  Geography  and  Historv       Onlv  in  „  f 
exceptional  schools  is  he  put  to  any  flire^ct^men  afwo^upon  tt  subiort' 
matter  of  Science,  or  taught  to  think  for  himself.     .     .      ^    The  ?  1,  o  o^ 

iTeKtse  f'^'£?hr  • 'i^  ''?  ^^'"''^^y  ^^  t«  incite  the%; '' ^"o 

neip  himselt.     Mechanical  school  work  can  give  instruction   h.,t  n-  Z„      I. 

develop  faculty,  because  this  depends  upon  seExeTS!    £ien^^^^ 

pursued,  IS  the  most  valuable  school  of  self -instruction    From  th^h^if  ^  •  ^ 

men  of  Science  have  been  «elf -dependent  an     S-VeUaTt  ^^^^^^^^^^^^ 

^h;^e^z:ij^'^^-'^-  ^'^y  '^^  bernt-o^st'idnrer'J; 

That  such  a  state  of  things  should  exist  is  not  to  be  wondered  at 
Any  eacher  knows  how  hard  it  is  to  dispossess  the  minds  of  students  of 
the  old  inherited  ideas  of  learning  from  books.  They  take  naturally 
enough  to  memorizing  a  page  of  text,  but  seev.  >o  have  no  other  ideas 
of  education.  They  are  bom  blind  (to  the  v  u  .d  of  natural  objects), 
and  unfortunately  have  been  taught  to  read  before  learning  to  see. 

The  system  of  education  pursued  for  generations  has  been  a  study 
of  words  rather  than  a  study  of  things.  Pupils  have  been  trained  to 
read  and  remember  what  others  have  written,  instead  of  being  trained 
to  ascertain  and  establish  what  is  true. 

Is  it  not  natural,  then,  that  we  should  find  them  not  independent 
seekers  after  knowledge,  but  merely  receptacles  of  information? 
Nevertheless,  hard  as  the  task  may  be  through  the  faults  of  our 
ancestors,  is  it  not  the  duty  of  the  teachers  of  to-day  to  train  their 
pupils  m  that  close  and  accurate  observation  which  develops  patiencv 


iv 


PREFACE   TO  THE   FOURTH   EDITION. 


and  cultivates  the  habit  of  mental  concentration  ?    Is  it  not  our  duty 
.8  It  not  our  privilege,  to  change  them  from  passive  and  imitative  to 
active  and  creative  ? 

hZZ^'^  7);«»bjects  are  so  suitable  for  this  purpose  as  physics  and 
biology.  But  even  with  these  subjects  the  teacher  of  elementary 
science  must  keep  constantly  in  mind  that  the  primarv  object  of  his 
work  ,s  mental  training,  while  the  acquisition  of  info'rmation  by  his 
pupils  IS  a  matter  of  only  secondary  consideration.  Pupils  having  an 
ap  itude  for  this  work  will  find  such  elementary  training  a  helpl" 
not  a  hindrance  in  their  advancement  as  specialists,  while  those  havinc, 
no  particular  aptitude  for  science  will  find  the  power  and  habit  o'^f 
fonmng  exact  conceptions,  which  they  have  gained  from  a  proper  study 
of  elementary  science,  of  incalculable  benefit,  whatever  walk  of  life 
they  may  follow.  They  will  leave  our  schools  with  hands  trained  to  do 
a  little  manual  work  well,  with  eyes  keen-sighted  enough  to  see  thin^^s 

XLIV    "^'  '^^^"^  '''''''  °^  ''^'"^-^^  "p-  *»>-  ^'^i-i^ 

About  four  years  ago  I  was  requested  to  prepare  a  work  on  Elemen- 
tary Physics  for  use  in  the  High  Schools  of  Ontario.     A   careful 
examination  of  all  the  works  of  the  kind  lately  published  in  England 
and  America  showed  that,  while  many  contained  well-selected  experi- 
ments logically  arranged,  none  could  be  used  as  a  text-book  without 
taking  from  the  pupil  nearly  every  opportunity  of  observing  and  of 
thinking  for  himself.    I  found  the  experiments  described,  the  attending 
phenomena  carefully  described,  and  the  conclusions  to  be  drawn  fully 
stated.     Often,  indeed,  the  experiment  was  given  merely  to  prove  to 
the  pupil  the  truth  of  a  statement  previously  made.     In  short    I  found 
many  capital  books  with  which  to  cram  pupils  with  information,  but 
none  which  seemed  to  me  entirely  suitable  for  mental  training.     The 
book  which  approached  nearest  to  my  idea  of  what  a  text-book  on 
Elementary  Physics  should  be,  was  the  "  Elements  of  Physics  "  bv 
Professor  Gage,  of  the  English  High  School,  Boston,  Mass.,  and  '  with 
the  consent  of  the  author,  I  have  made  it  the  basis  of  the  ''HL/h 
School  Physics."     Mr.  Gage's  experiments,  which  for  the  most  pal-t 
are  to  bo  made  by  the  pupil  himself,  I  have  retained,  making,  also  a  few 
additions.     But  m  place  of  descriptions  of  phenomena  and  statements 
of  conclusions.  I  have  substituted  suggestive.  <i.,o.tiong  t,>  he  answered 
by  the  pupil  after  he  has  made  the  experiments.     By  this  means  the 


PREFACE  TO   THE  FuUKTII   EDITION.  y 

pupils curi.,«.ty  i«  cjlistod  on  the  aide  uf  the  teacher.     Tlie  boy  .nakes 
ho  e.H,ornnentH,  and  observes  the  resultin,  phenon.na,  becaus      t 

Of  course  I  consider  the  experiments  and  questions  as  merely  tvnicil 
and  not  exhausfve      The  skilful  teacher  wUI  add  to  bX  I  S  urn 
stances  sho^.  may  be  desirable.     For  example,  a  wrong  answer.  venW 
a  pupd  to  one  of  the  questions  in  the  text-book  wUl  surest    .t  I 

Very  seldom  is  it  necessary  for  either  text-book  or  teacher  to  enun 
cate  observed  facts.     I  do  not  mean  to  say  that  the  pupil  will  gene  alW 
enunciate  observed  facts  correctly  and  fully;  far  from  T     Tut  the 

rrjirri  r'r""'"°"  ^"^  completlng'^e  enunclti on  ,-;  n ty 
the  pup.1,  should  by  experiments  and  questions,  point  out  the  e  rorl 
and  omissions  until  the  pupil  himself  constructs  a  perfect  enunciatLn 

in  the  next  process  in  the  study  of  physics  in  H,«  .^       ■       ■ 
and  c„„,,„iati.„  „,  natural  W.  a,  LJ^^'^^^,^       ;"';;: 

and  whieK  »e  are  .,.e.,„™  ,»„„,„  /JZ  ^rral.^lr"'""''' 

adanrc  and  jusUy  appreciate  the  fe.  «lrM  „d°„    tt    t  H     T   " 

TT.  ,  „  .  C.  Fkssendbn, 

High  School,  Napanee, 
March,  1889, 


COJSI  TENTS. 


CriAPTEli    I. 
MATTER  AND  ITS  PROPERTIES. 


Introduction.  —  Moloculo. 


I"  A  (in 


Coiistitiitioii  of  ni.'ittor.  — Physical 
and  dicmical  clian-es. -Korcc.  _  Throe  sk  of  matter.- 
rhenoniena  of  attraction, -adhesion,  colicsion,  etc.    ....      i 


CHAPTER   II. 
DYNAMICS. 
Dynamics  of  rtnids.-I'ressnre  in  lluids.  -  Daronieter. -Compres- 
sibility and  expansil.ility  of  iluids.  -  Transmittal  pressnre. - 
Siphon. -Apparatus  for  raisinjr  liquids.  -  Buoyant  force  of 
(luids.  -  Speciilc   ,«;ravity.  -  Motion.  -  Laws    of    motion.  - 
Composition  and  resolution  of  forces.  -  Center  of  -ravity.  - 
Curvilinear    motion.  -  .\ccelerated    and   retarde.l    motioi,  _ 
The    pen.hdnm. -Momentum. -Work   uud   eneri-y  -  Trms 

forn.ation  of  em-rj^y.  -  Machines, -K,,„ilihriun.  of  forces  in 
one  plan(> 


47 


CIIAPTKK   III. 

MOLECULAR  ENERGY.  -  HEAT. 

Heat   <I»«(lned.-Tem|.en.tnre.-l)ifiusion   of   Heal 
hei 


I'at. 


bodit 


Kxp.ansion, 


lOllects    of 


Th.-r 


iM.iiiietry.  —  Law; 


Luivs  of  rnslon  iiiul  Itoil 


oC    ii'a 


s(;ons 


I  US'-. 


potential  enerfj:y,  and 
dynamics.  —  SteMm-eniriue 


I  bat 


eonverlible  into 


rice  versa.  —  Spedllc  heat.  —  'i'| 


lermo 


i>< 


CONTENTS. 


I-Af: 


CHAPTEn    IV. 
ELECTRICITY  AND  MAaNETISM. 

f'"nvntdec,,n.i.y._l3atU.i.s.-Km.ts  pro.,,,ced  hy  elocMnc-ilv.' 
-  IMortncal  moasurcmonts.  -  Arn,^notsan,l  mni^notism.-  r.nvs 

<>  -.rronts.  _  Magneto-electric  and  cnrrcnt  hulnction.- 
I  l.<'.-n.o.,.lecf,rici.,v.  -Frictional  electricity.  -  Electrical  ma- 
chines.—Applications  of  olcctricily 

•     •     •  ^00 


•r'nAi»Ti;i{  V. 

SOUND. 
Vibmtion  an,l  waves.  -  Sonn.l-waves.  -  Velocity  of  sonn.l. 
flection  and  refraction  of  soun.l. -Loudness.  _  Piteh. 


bration  of  strings.  —Quality 


lie- 
Vi- 


20 1) 


CHAPTEK'   Vr. 

RADIANT  ENBROy- LIGHT. 

Introduction. —Pi,otonietrv.—Ke(le(ii..n       i.  .•      .■ 

^,  ,  '"•>•      ^'*^''<^Hi<>"—l{clraction.— Color. 

-Thermal  ertects  of  radiation.  -Optical  instrnn,cnts 


;j2i 


Ai'PKNnix 


ily. 
iws 

na- 


200 


2f)f) 


ELEMENTS   OF  I'TIYSKJS. 


;i2i 


37i") 


# 


B 


s 


ELEMENTS  OF  PHYSICS. 


CHAPTER   J. 
MATTER     AND     ITS     PROPERTIES. 


INTRODUCTION. 
Means  by  which  we  obtain  a  knowledge  of  Nature.  — 

W^„..o,„.o,M,lo,l  ,viil,  .n,.nn«Mfaninin,r..,  KnruvlPflaP  r.f  t,|„>  fllilios 

NOTES    AND    CORRECTIONS. 

and'^'^i.tiot"'"  '"'"  '^^"-'-I-e^t  "  permanent "  between  "in" 

Page  23.— Insert  foot-note     "Min,,   i:,.  t    i. 
ehem.cal  .lecomposition  beS  beco.ni.fg  lapors  »  '"°'*^  '"^'''^  ""^'^^'^^ 

Page  102  'I  lir  f""  ^T""^"^  "  ^^^^  "  '•^'^'j  "  CAH." 
i  age  178,  1  /  hnes  from  bottom. -For  "  161  "  read  "  18^  "  ' 

part  of  the  stroke."  ^        ""^     always"  read  "during  the  greater 

Page  109,  2  lines  from  bottom  -For  "h  .f  ^ 
<h^o.  to  the  heat  generated  in  tTe  fm-nace  "     ^^''"''  "'"^^     ''^^'^  "^''^-'fe'y 

I  age  220,  at  foot  of  page.  -Insert  "  nl.  ■ 
prove  the  truth  of  the  fo.Jgoing  statem^!;'"  '  "''"^  °^  experiments  to 

c^iS^^HHoJP'-^^''  "^"^*--'  Electricity"  read   "Electri.i- 


1 

We 

ahci 
Ilea 
we 

Olltl 

and 
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thrc 
edg 


II 

sens 

seer 

heai 

full 

neai 

hold 

twe( 

whe 

man 

whiz 

cxp( 

decc 


ELEMENTS  OF  PHYSICS. 


CHAPTER   I. 
MATTER     AND     ITS     PROPERTIES 


INTRODUCTION. 

Means  by  which  we  obtain  a  knowledge  of  Nature.  -  - 
We  are  provided  wilh  means  of  gaining  u  knowledge  of  the  things 
about  us.  We  hear  sounds,  we  see  light,  we  smell  odors,  we  fed 
heat,  we  feel  the  contact  of  other  things,  and  we  taste.  Thus 
we  have  six  gates  ihrough  which  information  concerning  the 
outside  world  may  reach  us.  These  gates  are  called  aeuses, 
and  any  information  received  through  one  of  them  is  called  a 
sensation.  Moreover,  we  Jave  the  power  of  reasoning;  and 
through  our  senses,  aided  by  reasoning,  we  acquire  what  knowl- 
edge of  Nature  we  can. 

OUU   SENSKS   SOMETIMKS    DECEIVE    US. 

It  must  not  be  forgotten  that  we  are  often  deceived  by  our 
senses,  or,  it  may  be,  by  our  reasoning.  We  believe  we  have 
seen  what  we  have  not  seen,  or  have  heard  what  we  have  not 
heard.  Thus  to  nearly  every  one,  perhaps  to  every  one,  the 
full  moon  appears  larger  when  near  the  horizon,  tlian  when 
nearly  overhead.  You  may  i)rove  that  this  is  an  illusion  by 
holding  a  five-cent  piece  at  arm's-Ieng.h,  nearly  in  a  line  be- 
tween your  eye  and  the  moon  in  the  two  positions.  Again, 
when  that  beautiful  meteorite  shot  across  the  sky  in  June,  1884, 
many  who  saw  it  afflrmeU  afterwards  that  they  had  heard  it 
whiz,  while  others,  having  quite  as  acpte  a  sense  of  hearing, 
experienced  no  such  sensation.  Doubtless,  the  former  were 
deceived  through  mistaking  the  meteorite  for  a  rocket.    As  they 


i  I 


2  MATTER   AXD   ITS   PHOPKRTrES. 

Imd  always  heard  .  .oc-ket  win.,  tl.ov  infenvd  that  the  ,neteor- 
e    1.  11  kew,.e.      Jt  .  pn,vo..|.ial  that  a  stc.-y  changes  wondc- 

fnll3  as       pHHsc-s  fron.  m.n.th  to  nu.nlh,  an.l  U.is  has  boon  set 

dawn..tho  ef^et  of   n^o.al  depravlt.   in   n.nlvind.     ,U.t  i^^ 
her  the  elFect  c,f  nnxing  n,.  inleronc-es  with  sonsa.ions.     The 
ndcntof  natnre,  ifhe  is  to  snceee.l,  nn.st  lean.,  an.on..  oth 
•ngs,  not  to  allow  unconseions  inferenee  to  take   the  ^he     , 

'jbservation.  ' 

OUDKU   OF   NATURK. 

t  em.  t  ,1  c.  p...  .„  ,u  a  reg,,!,,,.  „,,!,,.   ,„„|  tl,,,!  „,„„„  e,,,,^™  ,„-o 

of   1.0.C  „l,o  Lave  g.,„o  heforc  l,i,u,    c-a„„ot  l,„t  I Lk-vo    h 
-*'».'/  /-.,v««  ',y  c./,„„c.c..     ,t  ,s  „,e  „,„,„.,,  „,  ,,^, .  ,^,  7^ 
".v.-»t,ga,.  ll„s  „r,lc.,-  .,f  nature.      M„d,  l,a.  b.cu  done,     , 
liiucli  iiK.ic  ifiiiaiiis  to  l,e  doii,..  ' 

A    LAW   OF   NATUHK. 

When  we  have  discovered  a  fact  co„eer„ing  ,l,e  order  of 

We  btato  a  law  ot  Nat,ue   a»   fully  aud   precisely   a»   wc   are 
acqua,nted  w,th  the  facts  of  which  it  is  a  s.atcnent.      ^  rth  r 

anothu  foi  ,t.     Ihus,  long  ago,  "  Natuie   abhors   a  vacnum  " 

was  g,vc„  ^  a  law  of  Natnre,  and  was  based  on  snch  ,        ■",. 

o..»  -   -   been  ,n.ade  np  to  that  tinte.      Hnf  further  oh        . . 

a:;i:'i:"'""   ■™"    ''""^' ore  hereafter,    led   „.„    to 

A    LA„    OK   NATURE    IS   NOT   A   CADSE. 

ecm-se.    When  Newton,  from  seeing  an  apple  fall  in  his  orchard 
"s  le,l,  tron,    further  observation    and  powerful   reasonh;'' 


1 

i 

■'\. 

to  ec 

the  c 

covei 

i 

i 

town 
will 

fiXPEHIi\[ENTATrON. 


3 


to  enunciate  the  sublime  law  of  gravitation,  he  did  not  discover 
the  cau3e  of  the  falling.  No  one  since  Newton's  time  has  dis- 
covered the  canse  of  a  tendency  on  the  pnrt  of  bodies  to  move 
toward  one  another,  and  it  may  be  donl)ted  whether  any  one 
will  ever  discover  that  cause. 

MATTKU    AND    PIIKNOMENA. 

It  nrrs  been  sai.l  that  any  information  of  the  world  abont  ns 
tiiat  we  receive  through  our  senses  is  called  a  sensation.     That 
which,  acting  on  our  sensiferous  organs,  may  produce  a  sen- 
sation is  calle.1  a  natural  i>henomevon.     Again,    the  source  of 
all  natural  phenomena  is  matter.     You   have  a  sensation  that 
causes  yon  to  say  that  you  see  a  rod-hot  ball.     The  licrlit  which 
acting  on  the  sensiferous  organs,  produces  the  sonsa°tion,   is  a 
natural  i.henomenon.     The  ball  itself,  which  is   the    source  of 
the  light,  is  a  portion  of  matter.     In  short,  amjthinq  you  can 
see,  anythfnrj  you  can  smell,  anything  you  can  feel,   anything  you 
can  hear,  amjthimj  you  can  ta-tc,  is  matter, 

MATTER    MUST    BK    PISTINGUISIIKD    FROM    PHENOMKNA. 

You    must  be   careful    not    to   confound   matter   with   any 
phenomenon  of  which  it  is  the  source.     Sound  is   not  matter  • 
but  a  bell,  (,r  anything  else  that  may  be  the  source  of  sound   is' 
matter.    Light  is  not  matter ;  but  the  sun,  or  anything  else  that 
may  be  the  source  of  light,  is  matter.    An  odor  is  not  matter  • 
but  a  p.ece  of  musk,  or  anything  else  that  may  be  the   source' 
of  odor,  IS  matter.     A  flavor  is  not  matter ;  but  a  piece  of 
cinnamon,  or  anything  else  that  m.y  be  the  source  of  a  fl-ivor 
IS  matter.     Heat  is  not  matter;  but  the  flame  of  a  candle,  o.' 
imythmg  else  that  may  be  the  source  of  heat,  is  matter      Pni,, 
IS  not  matter;  but  a  sharp  thorn,  or  anything  else  that  may'be 
llu.  Hourrr  of  i)ain,  is  matter.  ^ 

§  1.  Experimentation.  ~W,  observe  phenomena  which  arise 
from  natural  conditions ;  that  is,  from  conditions  with  which 
man  Las  nothing  to  do,  and  we   may  learu  h   from  such 


■*  MATTKU   AM)   ITS   iMJOl'KItTlES. 

Observations  if  they  are  carefully   attended   to.     But  we  may 
liave  some  doubt  concerning  the  exact  conditions  under  which  a 
certau,  phenomenon  arises.     We  then  bring  about  accurately 
known  artifical  conditions,  and  observe  the  phenomenon  arisiu<r 
Jn  this  way  our  knowledge  becomes  n.ore  accimUe  or  scientijic" 
It  IS  a  matter  of  co.nmon  observation  that  water  sometimes 
freezes,  and  that  it  fr.rzes  when  the  te.nperature  is  low.     By 
tnal  we  may  ascertain  the  exact  conditions  .nul.r  which  water 
changes  mto  ice.     Whenever  we  place  natural  objects  under 
certam  accurately  known   artificial  conditions,  for  the   purpose 
of  observu.g  the  resulting  phenomenon,  we  make  an  experiment 
n  IS,  of  course,  necessary  that  we  know  exactly  the  conditions 
present  ,n  any  experiment,  or  our  trial,   inste'ad  of  teachin-., 
will  deceive  us.     It  is  not  an  ensy  task  to  make  an  experiment 
and  properly  to  read  the  lesson  that  it  teaches,  because  it  is 
very  diflicult  to  exclude  all  conditions  whose  presence   we   do 
not  dcsu-e  ;  and  often  conditions  are  present  without  our  know- 
ledge. 

An  experiment  is  a  question  put  to  Nature.  We  receive 
the  answer  by  means  of  a  phenomenon;  that  is,  a  chancre 
which  we  observe,  sometimes  by  the  sight  or  hearmg,  sonre- 
times  by  other  senses.  In  every  experiment  certain  facts  or 
conditions  are  always  known;  and  the  inquirv  consists  in  as- 
certaining the  facts  or  conditions  that  follow  a;  a  consequence, 
liie  following  experiments  and  discussions  will  illustrate  :  _ 

§  2.     Things  known  and  things  to  be  ascertained  -  Wp 
are  certain  that  we  cannot  make  our  right  hand  occ«  sam 
pace   with   our  left  hand  at  the   same  time.     All  Experience 
teaches  us  that  no  t.o  portions  of  matter  can  occupy    ke  Zl 
space  at  tke  sam.  tin..     This  property  which  matteV  possess" 

tJ^ml:      'T"  '""  '^  ""■"  ^•'^^^^'  >^  -^"-5  -"/>-- 

The  of.  .  ''  T"'"  '''  ""'*"•'  "^^''^'"«-  ^'-  possesses  it. 
These  acts  being  known,  let  us  p-oceed  to  put  certain  inter- 
rogatories to  Nature.     Is  air  matter?     Is  a  vessel  full  of  Ir 


1 


THINGS   KNOWN   AND   To  JJK  ASCKllTAlNEl). 


5 


I 


Fig. 1. 


a  vessel  full  of  nothing?     Is  it  -  empty  "?     Qni  matter  exist  in 
an  invisible  state'/ 

Experim«.nt  1.     Float  a  cork  on  a  surface  of  water,  cover  it  witli  a 

tunihler,  or  tall  -lass  jar,  and  thrust  the  glass  vessel,  nioulh  downward 

nito  the  water.     In  case  a  tall  jar  (Fig.   1)    is  used,  the   experiment 

may  he  made  more  attractive  by  placing  on  the  cork 

a  lighted  candle.   Slate  hmv  the  experiment  answers 

each  of  the  aljove  questions,  and  wliat  evidence  it 

furnishes  that  air  is  matter;  or,  at  lca.st,  that  air  is 

like  matter. 

Experiment  2.  ii„ld  a  test-tube  for  a  minute 
over  the  mouth  of  a  bottle  containing  amuiouia- 
water.  Hold  another  tube  over  a  bottle  containing 
liydrochloric  acid.  The  tubes  become  tilled  with 
gases  that  rise  from  the  bottles,  yet  nothing  can 
be  seen  in  either  tube.  Place  the  mouth  of  the  first 
tube  over  the  mouth  of  the  second,  and  invert. 
Do  you  see  any  evidence  of  the  presence  of  matter? 
Was  this  matter  in  the  tubes  before  they  were 
brought  together?  If  not,  from  what  was  it  formed? 
Which  one  of  the  above  questions  does  this  experi- 
ment answer?    How  does  the  experiment  answer  it? 

Again,  we  are  quite  familiar  with  the  fact  that  matter  exertg  a 
downward  pressure  on  things  ui)on  which  it  rests  ;  and  tliat 
matter,  in  a  liquid  state,  at  least,  exerts  pressure  in  other  direc- 
tions than  downward,  as,  for  instance,  against  the  sides  of  the 
Fie.  2.  containing  vessel.     Dops  air  exert  pressure  ? 

Kxperiment  3.    Thrust  a  tnmbh^r,  mouth   down- 
ward, into  water,  and  slowly  invert.     You  see  bub- 
bles escape  from  the  mouth.      What  Is   this   that 
displaces  the  water,  and  forms  the  bubbles?    When 
the  tmnbler  becomes  fdleil  with   water,   once   more 
invert,  keeping  its  month  under  the  surface  of  the 
water,  and  raise  it  nearly  out  of  the  water,  as  in 
Figure  2.     Why  does  the  water  not  fall  out?     Wh.at 
would  happen  if  you  were   to  make  a  hole  in   the 
bottom  of  the  tmnbler?    Make  the  experiment  with  a 
glass  tunnel,   first  closing  the   small   .   u\  with  the  linger,   and   then 
removing  it     What  conclusion  do  you  draw  from  this? 


(] 


AIATTKIJ   AND    ITH   riU-.PRliTrKS. 


Fig.  3. 


'"'.«  I..  iL  „     ,01,,    .°    ,    '"  """"■■    '"■-"  "-  """-r 

o  '-I'-t-  lias  IE,      y/rt.s,  ,„^.  ^y(./^/^^r, 
Experiment.';.   Exiiaiist  tl.<>  .,!..  . 

stop-cock  to  pi-evont  th,.  r...t.  ,.         i"        '^"""  *"''"«'  "'« 

The  exporimcnts  with  n>r  toach  i,s  thnt  //  ,•  >  ..  ^^^ 
-nee,,,.  .na,,r,  It  can  ...lu^Z^ZXt  'n  ^^ 
occvines,  it  exerts  jve.vire   mnJ  ;  "^   "'  "^''^  'P"'''  '^ 

AN   INVISIBLE   STATE.  ^   "^  '  "^*^''   ^^^^^    EXIST   If, 

§  3.  Minuteness  Of  particles  Of  matter       p.     •  ,     . 

J'roatlio,  small  purtielos  of 
tli.'it  siiLstfinco  which   are 
floating  in   the   air.     The 
fi'f,     for    several     meters 
aroun.l,  is  so.netinies  filled 
"•ith  fragrance  from  a  rose. 
y''^  cannot  see  anythinir 
in  ^^  ^  -ir.  'uit  it  is,  never^ 

fine  dust  that  floa-.,  :u     ,  .,oa,  t! '. 

J«t  sea  renders  the   .'hon    '..r'l.  "• '""."  .  '^'"' "'^o'"  "^ '-osemarv 


FIff.  4. 


Fig.  5. 


iiil£' 


THE    MOLErrLE. 


1 


years,  by  constantly  semling  forth  into  the  air  a  dust  of  musk 
1  hoi.gli  tliu  nuaiber  of  partich's  that  owcapo  ninst  Ik;  eoiuitless, 
v».'t   th^.v   aru  so  .^auill  that   the  original    giaiu   doi's   not  losJ 
j)i'rc!('p<J>ly  ill  woigiit. 

Tho  init-roscoiH;  (.nahlt'.s  us  to  sec,  in  a  sing].,  (hoi)  of  sta-niant 
water,  a  world  of  living  creatures,  swimming  with  as  much  iil.erly 
as  whales  in  a  sea.     The  larger  i.rey  ui.un  the  smaller,  and  tho 
smaller  find  their  food  in  tlie  still  smaller,  and  so  on,  till  tho 
powx.r  of  the  microscope  fails  ns.     The  whale  and  the  minnow 
do  not  .hirer  more  in  siz.,  than  do  some  of  these  animalcules,  the 
largest  of  whi.h  are  har.Uy  visible  to  the  naked  eye.     But  -is 
the  smallest  of  these  perform  very  complex  oi.erations  in  col- 
lectmg  an.l  assimilating  food,  we  nmst  onclude  that  thoy  are 
eomp..sed   no.  only  of  many  parti.-les,   but  of  n.any  kinds  of 
matter.     These  minute  living  forms  that  p..ople  the  microscopic 
w..rl(     are   exceedingly    largv,   in   comparison   with    the   incon- 
ceivably nnnute  particles  called  molecuk,,  which  i.hysicists  now 
"  measure  without  seein<^" 

§4.    The  molecule. -Experiment  1.  Examine  carefully  a  (h-on 
of  water  w.tl.  t  e  nakeC  c, .,  or  wiU.  a  nncroscope.     So  f^v^^H^ 

mifU  with  wahT.     Fill  a  test-tul.e  with  wafer  (Fi-r  «) 
Insert  a  cork  stopper,  pierced  with  a  jjlass  tube ;  heat 
over  a  lanip-flan.e,  au.l  note  the  phenomena  produce.l 
Describe  the  result.     Place  it  in  ice-water.     What  hap- 


pen.' 


Kep.!at  this  experiment,  usin-  otiier  li.,ni.l.s,  an.l 

(»    fill*    »'j\o  111  t^ .,  _. 


compare  the  results 


This  change  of  volume 


can 


Expand- 
ed Btute. 


be   explained  only  on   one  of 

two    suppositions  :    the    space  contract 

occupied  by  the  water  rnay,  as    '" """" 

it   appears,  be   full   of  water,  ^^^^__ 

which  the  heat  causes  to  expand,  and  occupy  a  greater  space  as 

represented  giaphically  in  Figure  7  ;  or  the  body  of  water  may 


rig,  a 


Kxpancl- 

t'd  state. 


Which     Contract- 
ed atate. 


^  MATTER   AND   ITS   PROPERTIES. 

consist  of  a  dofuute  number  of  distinct  particles  culled  molecules 
(us  represented  in  Figure  8^    sen-ir-.h  rl  c.  molecules 

„„„„  „  'fe"i'-  o;,  scp.iiiited  Irom  ouy  another  bv 

spaces  so  small  as  not  to  be  perceptible,  ^ 

even  with  the  aid  of  a  microscope.     Expan- 
«ioii,  in  this  ease,  is  accounted  for  l)y  a  simple 
sei)aration  of  molecules  to  greater  distances. 
There  is  no  increase  in  the  number  of  mole- 
cules, no  increase  in  their  size,  only  an  en- 
I'irgement  of  sjmce  between  them.     Whiel 
of  these  sui,i)ositions  is  the  more  probable? 

Kxperlment  2.    Place  a  tinul,lcr  full  of  cohl 
water  in  a  war...  place,  and  ii.  about  a.i  hour 

l.a.s  doscenclocl  intL  to  li^La"  '    "'     ''  "'  '''"'"''"  '''''  -*«'^«  --' 

-;;i;::rh;i-^^^^^^^^^^^ 

«>>  the  wate,.      1|„H  seems  to  contradict  the  fn-st  of  the  above 

vatc,    s  fall  of  water,  leaving  no  roo.n  for  other  matter.     But 
ccordn.g  to  the  second  supposition,  the  space  is  not  fillea  w 
^vater;  there  .s  st.U  room  for  particles  of  other  matter  in  tlo 
spaces  among  the  molecules  of  water.     Now,  as  we  canno   co  ! 
o.ve  of  two  portions  of  u.atter  occupying  the   same  space  at 
tu,  same  tune   («.,.,  .here  air  is,   water  cannot  be),  we  co 
ude  that  the  glass  '^  full  of  water  "  is  not  full  of  water        n  a 
Hlar  ma..ner,  it  n.ay  be  shown   that  no  visible  body  con 
letely  fills  the  space  enclosed  by  its  surface,  but  that  there  a  . 
spaces  m  every  body  that  may  receive  foreigi  matter      If  the  o 
m-e  spaces,  then  the  bodies  of  u.ttor  tlu^t  our    yes  a/o  te" 
.n.tted   o  see  are  not  continuous,  as  space  ;s  continuous      B.^ 
every  v,sd>le  body  is  an  aggregation  of  a  countless  numbef  o 
Hei,arate  and  mdividual  bodies  called  molecule,. 


CONSTITUTION   OP   INFATTRR. 


IVrlbrm,  at  ^our  homes,  the  two  following  experiments  : 

Kiperinient  4.  PiilvcTize  oiic-half  of  a  toaspoouful  of  starch,  and 
l.oil  it  in  two  tal)lc.spoonfuls  of  water,  stirrinj,'  it  nieantinio.  What 
l.hcnomona  occnr?  What  do  they  teach?  What  becomes  of  tlie 
water  ? 

Kxperlmont  5.  Fill  a  bowl  half  full  with  peas  or  I)eans.  J.ist  cover 
tlieni  with  tepid  water,  and  wet  away  for  tlie  ni-lit.  Examine  iu  tlie 
morning.     What  phcuomena  do  you  observe  ?     Explain  each. 

Strictly  speaking,  are  bodies  of  mattiT  impenetrable?  What 
only  is  impenetrable  ?  When  you  drive  a  nail  into  wood,  do  yon 
make  the  two  bcxlies  oeeiip^'  the  .same  spaee  at  the  same  time? 
Do  the  wckkI  and  the  iron  occupy  the  same  space?  How  only 
can  you  explain  this  phenomenon,  consistently  with  the  i)nnci- 
l)les  of  impenetrability  of  matter? 

§  5.  Theory  of  the  constitution  of  matter.  —  For  reasons 
whi<'ii  ai)pear  al)ove,  together  with  many  others  that  will  appear 
as  our  knowledge  of  matter  is  extended,  physicists  have  gener- 
ally adopted  the  following  theory  of  the  constitution  (jf  matter. 
Evenj  visible  hodij  of  matter  is  composed  of  exeeedimjhj  small 
particles,  called  molecules;  in  other  ivords,  every  bodi/  is  the  sum 
of  its  molecules.     Xo  two  molecules  of  matter  in  the  universe  are 
in  contact  with  each  other.     Erer>/  molecule  of  a  bod;/  is  separated 
from  its  neighbors,  on  all  sides,  by  income ivabhj  'small  spaces. 
Every  molecule  is  in  quiverinrf  motion  in  its  little  space,  moving 
back  and  forth  betiveen  its  neighbors,  and  rebounding  from  them. 
When  we  heat  a  body  we  simply  cause  the  molecules  to  move  more 
rapidly  through  their  .spaces;  so  they  strike  harder  blows  on  their 
neighbors,  and  usually  push  them  away  a  very  little;  hence,  the 
size  of  the  body  increases. 

This  theory  seems,  at  first,  little  more  than  an  extravagant 
gues3.  But  if  it  shall  be  found  that  this  theory,  and  no  other 
theory  that  1ms  been  proposed,  will  enable  U8  to  account  for 
most  of  the  known  i)henomena  of  matter,  then  we  shall  be  con- 
tent to  adopt  it  till  a  better  can  be  produced. 


10 


MATTER   AND  ITS   PROPEHTIES. 


§  6.  Porosity.  —If  the  molecules  nf  n  u   . 
^^l^^olute  contact,  it  follows  ^^fc    ,'  .  ""'^^^ ""''  nowhere  in 

among,  them  which  may  bo  occm  ic        '  '''"I    ""^^'^"l^'^'^l   «l>nce,s 
«taiu,es.     These  spaces  are     "  '  "'"''''''''  '''  '^'■'-''-  -"> 

^•Joth  and  beans.  It  is  Zalt^ 'T'  '''^''''  ^'''^''l'P--«  i" 
-ters  the  vacant  .paco'Lt^r;'"''  """"  '  '"'^  '^  --"v 
-"stances.  All  matted  i  '^  ^  7"  ""'  ""^'^^'"'^^■^^  «^'"-- 
t'"-o..oh  solid  cast-iron  .nd  IT  '  I?  ''''^''"  '"=^^^-  ^''  f^''^'^'^! 
!--'y,nuch  as  cha;^w^nV^:r  ^^  T"'  ^"^^^"'  ^'^''  '''^"'^^ 
•s  restrictcl  to  the  invisible  ^^uJ  '"  '"''''  '"  ^'''^^i-, 

c-avities  that  nmv  be  seen  in  '''''"'"^"  '"<>lc-enlcs.     The 

t"^'  --0  no  .norc^^i;  i^'t:  IL^!:':^^  '^''^  "'^'  1--'  '>"^  ^'oles 
J'one3-con>b,  or  the  room    of      1  o     '  ^"^■"'  '''^"'  ^''^'  ^-'"«  of  a 
••~.  the  pores  Of  the  :^^^^^^^^^^^^^ 

CKsl  has  s„occ.eclc.cl  ha  nscer^i    '.•'''''  ^■'"'•'"'^^'^•'.s,  the  phys 

-'"1 ..  it  is  thought  (hit  iLs      :  .e      i'  "•  ':'i'^"""-'  ^^>  ti-  «i.o  Of  the 
"i;P'^"-     I"  other  words,  tV      olee  '  "'''''"'  '"'■'''^'^-  ^''a..  u,/ 

What  an  apple  is  to  the  Jarth  ,  '".T"'  ''  '''  ''  "''•^l'  «'•  ^ut 

^-  or„.o,ecu.es  i„  .  ,,,,  La   Z:^':^^'''''^^^  ^'>  --'t  the  nu.n! 
'  ^<^^"'nl.  we  shonl.1  require  S.O.OOo""';;.;:  '  '     "  *""  '"'  """'«"  '" 

-^l^^"f5!^;^'':L:i:\;^^  ;vood,  apple,  p.,tv, 

volumos  „f  ,|i,n,,,,„t  (.,»,,  .„,„       '  '■"■''-  ""  "■'•'fl'l»  <>ni„.  „,„,„! 
-a.,o,.s  for  boli„vi„g  Sl    I,       i''t'  """"^  '■'"'•"-'  !■- 

liointiiro  nr,.  t|,s  -amo     W  i'         °  1""«ssimi;  ,in<l  tl,,.  i^,„_ 

matt..,,  in  „si„.„  :,„„;,  .i,;;*;^;';™'  «■';'  »<>".«  MU.  |,„vo  ,„„,.„ 

---«H:.M,H,..™.,.c:;,:;:::~;;nt:;- 


nowhere  in 

ol'itT  sub- 
fippL'ars  in 
It  it  really 
L'H  of  these 
'>e  forced 
till!  liv^uid 
I'  p'O'sics, 
I»'s.     The 
>iit  holes  ; 
cflls  of  a 
JO  called, 
e. 

■i>i"U  with 
Ik'  pliysi- 
It'  size  of 
ize  of  tho 
■  ''Jiiiii  an 
of  Water 
tlie  iiiim- 
ullioii  iu 


putty, 

I'y  have 

di'fer- 

•  4  and 
B  satne 
St  has 
eenles 
>  tprn> 
!  more 
E'ciiles 
'0  call 


SIM1>LE  AND   COiMPOUNr)   StJBSTANCES.  H 

thorn  more  cleiise.     By  the  «?«<!«  nf  „  k    i 

j'j  LUL,  mas.9  oj  a  bony  we  inidorst-inrl  tha 

5  8  Simple  and  compound  substances.  -  Plaoo  a  sm^ill 
.,..-. y  ,„•  .„,„„.  „„  a  „„t  «tovo.     I„  a  few  n.inaU.      cL™: 
to  a  black  ,„a...     Tl,i,  l,la,.k  «„,«ta„co  is  f„,„„,  ,„  ,,o  ,|,a,. 
o»l,  or  carbo,,,  „„  Ccnist.  call  it.     Evklcntlj-  the  s,„,a,.  ,„,,t 
...  oonta.no.    ca,l,o,„  fo,-  U,o  o.arl,„„  came  fro.n  tiro  ..J 
n,c.a,st,  aro  also  abl„  to  obtai,.  w.aUT  f.-om  ,„j;.ar.     Tl,c  I,:" 
m  our  «po,.„uo„t,  cxpclx  tbo  water  i„  the  f„n„  of  .,tea,„,  ami 
Ie.ave»  tho  earbo,,.      Carbo,,  can   be  ,..xtraet,.,l  from  JJZ 
other  ,vav.     Prepare  a  very  tl,ick  s.vr..p.  l-V  .li.«olvi„gC" 
ot  wa  er,  a,„l  p„„r  „po„  the  syrup  t,vo  or  three  thue.  it 

.'irr:;!';;;::."  """■ "-"  -'"  ''''''^- "'"»'"  -  "•*^- '.«-« 

By  mutable  processes,  there  may  be  obtained   from  marble 

dm  III  "'  "  "'"'■''°"  ■  "'""'""•  '^  ■•'  "'«"  "•tiled  cal- 

uum,  „lne,  looks  very  ,„„ch  like  silver ,  the  third  Is  a  gas  called 

ox-yge,,,  winch,  when  set  free  fron.  its  prison-house  i„t  .,1 

lib!:;;:.:,.  "'""^' """ '"" ^'^^ "^ ">" ■'""■^'" f™" -vi-i' h™ 

If  ivc  should  grind  a  s.uall  piece  of  marble  for  many  h„n,.s  in 

•stni,  each  little  pa.it'  ^f :;::.;.: !  •;:':,;  rXm.n'.bi;:':.'',r- 

<>n.g".al  hnnp.     If  we  .,h„ul,l  couli ,„..  ,,„  '         "  "  « 

:e;r.:"L::r„r;: ;-; .--:.i:;;i;.:;'r:;;;::i;i 

"-AjKit  lo   nnd   iill    Iho  rnn  ecu  cs    iimt   .iliI-M       v 

-.allct  piece,  our  u.olecnle.  our  ni;!  l;''  t  H.le'  ," '  X  a",:; 

Bince  „,,„.ble  is  co,np„„.d  ,„•  tl -ee  sni 


*  i 


^•'uni,  and  oxyjren,  we  c.nelnde  tl „..  ,„„ 

capable  of  division.     No  one  has  been  able 


>.sf!ui('o,s,  carbon,  eal- 

i.'tt  our  molecule  K.self  must  bo 

to  separate  any  one 


12 


MATTER  ANn  ITS   PIIOPERTIES. 


m 


Hi '' 


These  ^bstancosS'li"  1^;    .T^."  """  °-^-~S™- 
"l>  into  oU,or  substances  -nv!      n^  °''"'  '"  '"""k  "'em 

■"-ts.     Those  sntlwL   LT  T'*''  ■""■*""•"■'  <>''  "'<- 

:'---  a.  ea,K,  ^Z^T J^Z'^o"  ^^  '"^^  "«- 
l)er  of  sMl)staiice8  known  to  in-,,,  t.'  "'"  '■■"S"  nnni- 

other  snbstaaeos  are  el:,,    i    of    '         ""  "'""™"-     ^" 
clemento.  nipounils  of  two  or  more  of  tliese  71 

"Ot  lose  tla.ir^l,au    :.'*:„:::  T"">-.""-"  •••"•■"■'•  ^'^  "o 
l'""P-     Snd,  a  divi,ion7sc"Ulo,,       '"■■;•' •'''''•■''' "'"■'^'»»  ""' 

In  o</,«.  !,„,, ,/;;::";  * ;  ••" ««« '■' '» '-  ,■<»  *„,«, 

llieraselves  arc  <iivide,I  •  and  ,!■,!„    '  ,'"»•■"■'  "'"  "'°''^«"l™ 

«.bstanoes.  carbon  a^    at  r      nj"  '  "?"'""''  '""  *«  '>'" 
sngarno  longer  ovists  •  otil,  L, ,  ,      ■'"■''°"""*''  '»  'lestroje,!  • 

Tbemoieenlcof  s    tist!  „        n""?'  ""™  ""«■"  "»  l''"-- 

H '-  be,.,,  se„a,,:;i  tbar::, '  • '  ,t  i;;:r;t  -  'r  ^^w^'" 

pose  it.     Such  a  division  is  ...UnV       ,  ''"'''""  ^'"'^'^  <'«'»- 

these  c.han..o.s  the  substa     ;    I       io    ;;'''', '""''""  '^"""-     I>"'-i".'^ 
ha«  "oen  only  a  eha,,..,  ,n.^^:        ,  "^  '""'  "'•^  ""<■  <''"u.i,red.     T).,.,-e 

a  vc-y  intense  heat,  the    ^     ;"•;;, fj    ',    ^""  ■'^^--'  ''^  -hje.tecUo 

•■^  that  it  Ijecoines  eonverted  into  a 


f 


lias  taken 
iictcd   from 
>-\Vgen. 
break  thojn 
t'<^-'>'  or  ele- 
i'lto  other 
lai'ge  mini- 
Diits.     All 

these  71 

^,  is  that 
d  toithout 


sugar  is 
t,  but  do 
'et  as  th(> 
eiierally, 
ide7Uitf/, 
physical 
loleciiles 
<Hvide(l, 
the  two 
itroyed  ; 
s  phico. 
o  which 
at  coni- 
(Jeiier- 
'iontitf/, 

RtOilii), 

During 

'i'licre 

rraii^e- 

cted  to 

into  a 


ANNIHILATION  AND  CREATION   OF  MATTER.  13 

mixed  gas,  consistinj,  of  two  gases,  oxygen  aud  hydrogen.    This  gas 
IS  not   c.ndensable  at  any  ordinary  ten.perature.      Unlike  steam,  it 
burns  and  even  explodes.     What  kind  of  separation  is  this  ?     Wha 
has  been  separated  ? 

Blackboard  erayons  are  prepared  by  subjecting  the  dust  of  plaster 
of  Par,s  to  great  pressure,  which  causes  the  particles  to  unite  and  form 
the  crayon.  AM.at  kind  of  change  is  this?  What  kind  of  union?  In  the 
experiment  (page  5)  with  the  mnmonia  and  hydrochloiic-acid  gases 
the  two  gases  disappear,  and  a  solid  is  left  in  their  place.  Wliat  kind 
of  change  is  this :  chemical  or  physical?    Is  it  union  or  separation? 

>;  10.  Annihilation  and  creation  of  matter  impossible. 
—  KxiKTJiiieiit  1.  Prepare  a  saturated  solution  of  calcium  chloride' 
Mix  Willi  an  e(|ual  bulk  of  water  and  weigh  the  „(,lution.  Prepare  a 
dilute  .solution  of  sulpluiric  acid  (1  to  4j,  ami  pcmr  an  ecpial  weiglit  of 
the  last  solution  on  the  lirst,  all  at  once,  and  shake  gently.  Ins^,antly 
(he  mixed  li.,uid  becomes  a  solid.  The  solid  formed  is  connnonly 
called  plaster  of  Paris.  It  is  an  entirely  diflcrent  substance  from 
either  of  the  two  li(|ui(ls  used.  What  kind  of  change  is  tliis  ?  A  new 
substance  has  been  formed.  Has  matter  been  created  ?  Weigh  the 
'.•esulting  solid;  compare  its  weight  with  the  sum  of  the  weights^of  the 
two  li(|uids.     What  do  you  (ind?     What  conclusion  do  you  draw. 

Solids  may  be  converted  into  lujiiids  or  gases  ;  gases  may  be 
converted  into  li(|uids  or  solids  ;  substances  nuiy  conii»letely  lo.se 
their  cluuiuttcristics  :  but  man  has  not  discovered  the  means  hif 
ivhich  a  single  violccule  of  maitcr  can  be  created  out  of  nothiny, 
or  by  ivhich  a  simjle  molecule  of  nuttier  can  be  reduced  to 
nothinr/.  Midivv  cannot  be  created,  cannot  be  annihilated  ;  it 
is  a  constant  (inantity.  The  discovery  of  this  fact  laitl  tlie 
fonndation  of  the  science  of  Chemistry. 

This  statement  nuiy  not  seem  to  accord  with  many  occurrences  of 
every-day  exi)erieuce.  Wood,  coal,  and  other  substances  bin-n  ;  matter 
disapi)ears,  and  very  little  is  left  that  can  ijc  seen.  Hut  does  matter 
pass  out  of  existence  when  it  disappears  ir.  burning,  or  does  It  assume 
the  invisible  state  known  l)y  tiie  name  of  jras  ? 

Experiment  2.  Hold  a  cold,  dry  tumbler  over  a  candle-flame.  The 
bright  glass  instantly  becomes  dimmed;  and,  on  close  examination,  you 
find  the  glass  bedewed  with  (hie  drops  of  a  Ikjukl.   This  lUjuid  is  water. 


14 


"'""'"  '>'•'  '"  <•."..•«„.„«,. 


Voii  may  ,/,,,  ,^  ,^  HtrflH*,..  n    , 

>;'^/'.i-i."i.....x...:::  1^:^ -^-  '^^^^^^ «.. «.  not  n.... 

:.  •;•'"  "'wuyH  .tanw.  ov.;S  j;     :;;''-  "^"  '"-^'o  «a,„o  nat.M-o'' 
'<  »a.,..r  „f  the  riv<.r  mn«  a  .M      ,.  /  of  k?;';  ""  "•"  ^'-^--^-t  clays 

:f''^^p^^^^  ^"^"  "  Conn  „a.s  .ottle- 

'y- '"..I  Hhak..    a;«o  pour  C  J!r       ;      '"*''  *''*-'  '"""^''  ^"vor  ti. 

'"t  all   tin,  ,„v|„iM.,  /S,\u     't'    r      '"^'   ""^  ""»y   tl.e  a.sl  e 
•^  '•""".•  .i.at  their  collec'tl  rj :,;      ;:;;:""""":'>'  /-^"nncl,  alu 
Watordor-H  not  duhm  nni  /.#-      i 

Nat......  ,.  ever  array,  J tr,:?'^^'  ^'"  """""""'  "-I      0    aU 

-  air.  IH  .■..,.„„.,,.,,.,.,  4  » L.         ',  i*:,;;:''''''!''   ""-■  vapor  rise.  i„ 

'-'ocea,.  whence  It  can.,.     (; "'l     f/'*' ''''''  ''"'"''"'^  '"  'ivers  to 

oco«„H,un,|  even  the  ^' v^urU^^^l^Vr  '"*  ^''"''  '•"..Mn.nt.s  a.m 

well  «H  whole  t,-ll,e«  of  «,S«.'    ''''''''  '^  ''"-"'  """  ''""ay  a s 

;;•  -.nte.|  an,o,.«  the  ,|      ^LV"^^^^^^^^^  ^"I ue  ^;..;: 

that,  havo  crnn.bh.l  l/.todn.t    «.  i  n  '"'"'  ""'  '""'I'^h  will    ere 

t'-  '/"^«^'V  or  ..mtter  rej^,  „*,  1,  l^;^.;;^  '"^^'""^  '«  ^'-V.npt.     Only 


Force. 


15 


'lot  flamo; 
■■     If  water 
not  set-  i(  ? 
^•isihle  gas 
•out  of  the 
floating  in 
fiatdio.     A 
rt'st  days, 
king  a  bed 
Jst,  wljioh 

«s  bottle; 
ly  does  it 
t  was  be- 
vtT  tight- 
ir.  What 
(;nt  sJiow 
?  If  so, 
of  sight 

eel  vvliile 
^  aslies, 
inewhat 
I,  and  it 
t  which 

nor  are 
y^vhcre 
lysit-'al. 
ns   tlie 
ises  in 
crs  to 
ts  and 
•ay,  as 
L'  may 
1,   ere 
nposo 

I'll  wo 
Only 


§11.    Force.  — Experiment  1.   From  a  piece  of  rardhnnr,!  ..,. 
peud,  by  a,^,  „,  .ut  tL^-caUs,  .,.  p,,,,,,,,',,  ^  t^Trl;i, 

about  2""'  apart.  Procure  a 
clean,  dry  glass  tube,  about 
40'^"'  long  and  3""  in  diam- 
eter. Hub  a  portion  of  this 
tube  briskly  with  a  silk  hand- 
kerchief, and  hold  it  about 
2''"'  below  the  balls.  The  balls 
seem  to  become  suddenly  pos- 
sessed of  life.  They  gather 
about  the  rod,  and  strive  to 
reach  it.  If  we  cut  one  of 
.    ,  , ,  ,      .  t'lc  threads,  the  ball  will  flv 

straiglit  to  the  rod,  and  cling  to  it  for  a  time.    The  n,eans  by  which 
lie  rod  pulls  the  balls  is  invisible.     Vet  evidence  is  positive  that  the 
H.d  has  an  mfluence  on  the  balls,  -that  it  pnlls  then..     Slip  a  piece  of 
g^ss  between  tl;e  ro<l  an<l  the  balls;  still  the  in.luence  is  felt  by  the 

^.^^:^'''  ""^^^^^^  "'^  '''''''''  '^"-'«  "'^^  — ^  the 
Now  slowly  bring  the  rod  near  the  balls,  till  they  touch.     They  at 

1.-st  chng  to  the  rod;    but  soon  the  rod,  as  if  displeased  with  theiJ 
company,  begn.s  to  push  them  away.     Withdraw  the  rod;   the  b^ 
<lo  not  hang  by  parallel  threads  as  before,  but  appear  to  be     us  h 
one  another  apart.     Gradually  bring  the  pahn  of  the  hand  up  be     a  f, 
the  balls,  but  without  touching  them.     The  balls  .M-adu'ill        . 
;'.<•  Pnil.of  the   hand,  and  con>e   together.     Hem,;  t  "L  c  '  and 

hoy  ag^n.  fly  apart.     Matter  does  not  seem  to  bo  the  dca      1^ 
tlMug  winch  it  is  often  called ;  it  can  push  an.l  puu. 

Kxperln.ont  2.   Haise  one  of  these  balls  with  the  fingers  and  then 
w.   H  raw  the  fingers.     Something  from  below  seen.s  t<,CclM,      an 
I."  1  the  ball  <lown  again.     The  san.e  happens  with  <^^ch  o,  e  o^  Tl  o 

uu  ba  N.     Cairy  the  balls  ivto  another  room,  the  same  thin-  occurs 
Ca,-ry   hem  to  any  part  of  the  earth,  the  san.e  thing  ore       "  It  m  si 
bo  that  ,t  ,s  the  earth  itself  that  pulls  the  balls.     The  .'rt^i  p,  ,       '^ 
fnut  and  the  leaf  from  the  tree  to  Itself;  it  pulls  all  obj"       o  ,  .c 
and  more,      it  holds  them  there.     Attempt  to  raise  any  thin'  fron  t  u'. 
jrround,  an.l  you  feel  the  earth's  pull  resistin-r  you 

Attempt  to  break  a  string,  or  crush  a  piece  of  chalk,  and  you  find 
•  Tables  of  the  Metric  MeaBuroB  may  bo  found  i„  the  Appendix.  Section  A. 


10 


MATTKFl   AND   ITS    lUlOPEnTIES. 


t„  «1»,  ,„„  a„„,„p.  ,„  4:,:;;,",;;^;™"»  '°  koep  tu™,  t„g„,„„,  and 

vJi^K.TZ^ft"^-'^''  *™'^°°y  '°  P-'h  ™o  to 

"or  why  ."^      »«-■    .s   called  force.      We  do   not 

another,  or  to  separate  from  one  anZl     We  do  37        7° 
nature  of  force-    wo  0..,.,.^^  "'e  do  not  know  the 

know  that  t      e  „,rt  h'  '""  ,"  ""'  '^'■•■"'"  '"'    '"'^  «""l"J' 

The  familiar  effet,  roll    ""      I- '"'■'"'"  ^-^^^  I™""™"- 

eausewe  attrihut    to  foree     wZ  ' ,  "  "  "'"""=  ^  '"••" 

mt,  we  l„o]<  for  a  oa„s     ^nd  „  T  "       ^'  '"  '"°"''"  ""'""^  *« 

dflinitio,,  that  has  heen  ^ve^is  ,  J^ ,    f  '"■"     '■°'"l"'^''^'"'i™ 

i;ni:n,  foret\;t,i;r':;:;z.^r"':r:;:,,rjr'';- ^ 

A  pushi.,,  force  is  caiied  a  „,.l,„  f::^:^"'^" 

Placn  the  roj  l„  a  »lh "  "  7,°  r,,  ,T  '""  "'  "'°  """•  """ 
Coos  the  .X|,erl,„.,,t,  prme  .  '  ..  T  "°'"  '°  ""  "^"''"1  ""J- 
or  to  „„t|,  „f  ,,„„  , fr;,''°  '"''"-';"'■;■«  "-'""«»  to  only  o„c 

"i«'-r  T'"  'r  •■■•■"'"' "■'■X":::f,:;;^r'"  """■"•"'" « ■■• 

All  att)  action  and  reiiulsion  betw^^r,  .mr.      4 
mutual.  ^  '^'"^^'^  different  portions  of  matter  are 

§14.  Molar  and  molecular  forces  —  Tho  n-i  i   , 

«.ev  ..ave  „,.t  to  J.':,  C"  ^tr  Z'.-Ttr '^l' ''r" 
.      we  pass  the  hand  several  times  over  the  part  of  the  rod 


MOLAR  AND  MOLECULAR  FORCES. 


17 


that  has  been  rubbed,  and  over  the  balls,  thej  quickly  surrender 
their  forces.  These  forces  arc  temporary.  They  are  called 
electric  forces,  and  their  cause  electricity.  The  attractive  force 
tiiat  draws  the  balls  to  the  earth  existed  before  the  experiment. 
No  manipulation  can  destroy  it  or  increase  it ;  it  is  eternal  and 
unchangeable,  and  exists  between  all  portions  of  matter.  This 
force  is  called  the /orce  of  gravity,  and  the  phenomenon  is  called 
ijravitution. 

We  ha-  3  seen  the  effects  of  attractive  and  repellent  forces, 
reaching  across  sensible  distances.  Have  we  any  evidence 
that  these  forces  exist  among  portions  of  matter,  at  insensible 
distances,  i.e.,  at  distances  too  short  to  be  perceived  by  our 
senses?  Stretch  a  piece  of  rubber;  you  realize  that  the^^  is  a 
force  resisting  you.  You  reason  that  *f  the  supposition  be  true, 
that  the  grains  or  molecules  that  compose  the  piece  of  rubber  do 
not  touch  each  other,  then  there  must  be  a  powerful  attractive 
force  reaching  across  the  spaces  between  tiic  molecules,  to 
prevent  their  separation.  After  stretching  the  rubber,  let  go 
one  end.  It  springs  back  to  its  original  form.  AVhat  is  the 
cause?  Compress  the  rubber ;  its  volume  is  diminished.  (Does 
this  confirm  our  supposition  respecting  the  granular  structui-e 
of  matter?)  Remove  the  pressure  ;  the  rubber  springs  back  to 
its  original  form.     What  is  the  cause? 

Every  body  of  matter,  with  the  possible  exception  of  the 
molecule,  whether  solid,  liquid,  or  gaseous,  may  bo  forced  into 
a  smaller  volume  by  pressure,  —  in  other  words,  matter  is  com- 
pressible.    When  pressure  is  removed,  the  body  expands  into 
nearly  or  quite   its  original  volume.     This  shows  two  things : 
(u-st,  that  the  matter  of  which  a  body  is  formed  does  not  really 
Jdl  all  the  space  ivhich  the  body  appears  to  occupy;  and,  second 
that  in  the  body  is  a  force,  tvhich,  acting  from  tvithin  outioard, 
resists  outward  pressure  tending  to  compress  it,  and  expands  the 
body  to  its  original  volume  when  pressure  is  removed.     This  is 
of  course,  a  repellent  force,  and  is  exerted  among  molecules^ 
tenduig  to  push  them  farther  apart. 


18 


AIATTKI.'   AXI>   ITS   I'ROI'KUTIEH. 


But  it  Jias  piovioMslv  boon  shown  tl.^f  fi         •      , 

effect,  when  two  fo.-cos  aet  on  ..  ,  ,  ''.^■''  ^'^'^  ^vJ.jit  is  ti,(. 
^-'t  two  bovs,  at  opposite  e  h  1  of  !'/',  ;"  '''"'"'■^^'  <l'>ectio„s> 
'-^''  P"^''  with  ec„  H    forc^      . ;  H   >  ''  '""''  ""  '"'''^-     ^'' 

J?'v.'.ter  force  is  n„„lic.(l      V  ,         <'"-«"^'t'on  in  which  the 

<^^;-i'ni-i^v,whi;'h:t,:;;::',-^^ 

science,  when   he  first   h...,.  ""''*'  '^  '"'-^^'""f''' in 

-"Other.     Jf  f,i„,  ;J      ■;  ^-".v  ;-ven,  ,lo  not  touc.h  one 

^he  thought  of  m^^u'X^  T'\  "'■  "•'"""  ^"'"'"-  ^^ 
tl.ewindsas.so„,„ch,h.l  "'   '""^"  '"'''''''  '^^^^'^y  kv 

Tiie  ancients,  perceivino-  tint   mnff 
-"-II   parts,   overcan^e    tln^   di^^e  1/'   '""•''  '"   '"""'^  "'^  ^^ 
"^"">te  particles  have  hooks  o',     ''   '"''P'^^^*".^   H'-'-t   the 
-"Other.    Onr  knowc  I<r       ,  ''  '''''''^'  '^''^'  ''^'^'l^  «"<' 

We  see  that  the  molecnle    of  ^      ''''"'""^'^'■^^'■^"^^'• 

.-vpart,  or  fron,  scpar.  i  ^1  •'  '"''  '^'^'''^   '•••'^'"   ^'"'i"^- 

-  also  kept  f^-on!  H^^:^;  "  .XrH'  ^""'^^"''^-^  '^^  =  ^"<^ 
'>.V  ->  ever-existing  repelh>nt^^  b  " '     T  T""'"''''  ''^'''^''^ 

«ible  distances  l)ctween  n.ol  1  ,         '  ^''''''  ^'^  -^  inse. 

/-•-.  When  fbr^  "r  e  f'  ".  '•  ""  ""  "^"^^'  -"'-"^-• 
t'-v  are  called  noZ  t^'ZoT.  V""''''  '"^^"-- 
^-ecs;   (2)ofn,olecniar  fSrees     "  '""^^'•^^^-"«  O  of  n.obr 


"•     '^"'^^"^^   STATES   OF   MATTER. 
s  15.  Matter  i)resont<s  JfcL^u-  •     ^i 
''■'/««,  .,,,,1  ,wJ„,,,"':i     °   .  ;;  ""7;li'r-.o..t.,tn,o,:  .WM, 

-K.io„t  i,i,ii„,,,„i.,,,  I V ,,  air'nT "'"' "' "•■""■  -""■ 

"■'tu..„„i,uiga,osof„i,..     0„  Uus  account 


THltEE   STATES   OF   MATTER. 


19 


they  called  thorn,  to,.:c.lh..r  with  fi..,  ck.nents  or  pri.narv  matter. 
Ihcy  rannot  now  he  .so  regariled  IVoin  a  eheniical  point  of  view 
bec.au.se  each  of  then,  ha.s  heen  sei,an.te,l  into  still  n.ore  simple 
substances;  „or  fron.  a  physical  stan,|j,oint,  because,  as  will 
soon  be  shown,  most  substances  amy  exist  in  auy  one  of  these 
states. 

i;'  16.  Characteristics  of  each  of  these  states 
O.MHTi.n.nt  1.  ITovide  two  vessels,  a  cubical  dish  ami  a  jjoblet 
e  d.  luun  ,  a  capacity  of  about  200-.,  Also  provi.Ie  200™n. ,,(  ,,  '  ' 
in.)-,  of  water,  a.ul  a  cubical  block  of  wood  containing.-  200-' 
G msp  the  block,  and  place  it  in  the  cubical  vessel.  Atten.pt  to  do  the 
san...  hn.^^  w.lh  the  water.  Why  ca..  you  not  ..n-asp  the  water  ?  Pour 
a  port-on  of  the  water  n.to  the  cubical  vessel.  When  you  move  a  por 
tH,u  of  the  block,  the  whole  l>,ock  uk,vcs.     When  you  pour  a^ort^  . 

\\  1  y  s  this  ^    Why  .s  .t  that  we  can  dip  a  cup.ul  of  water  out  of  a 
P  -If ul,  without  raisin,,  the  whole?    Pou,-  all  the  water  into  .he  ^o  let 
he  water  adapts  itself  to  the  shape  of  the  goblet,  and  the  vesse  lis 
tilled.     Attempt  to  place  the  block  of  wood  in  the  ,.,blet.     What  dif- 

^Z  .'"f '""";' '" '""  "'•"'""  •  '"''^y  ""•^'  '""•--»-  ?  Vo  r 

e  w  ""v  "T"'  '"  ''""•'•     "  '""^'^*'^  ''''''  t«  the  shape  of  each 

ossel.    Why?    Drop  the  bh,ck  of  wood  on  a  table.    Pour  water  on  the 
tul^e.    How  does  a  IKpud  behave  when  there  is  no  vessc     o  cou  in" 

Kxperl.„ont  2.  Throw  small  particles  of  sawdust  into  the  «ol  et  of 
^vate. ;  you  can  thus  reu.ler  perceptil,le  any  n.otiou  of  the  water  in  the 
joblet.  Just  as,  by  thn.wiu,  blocks  of  wood  on  the  sn.ootl   .tfaco  ' 
a     ver   you  can  discover  the  n.otion  of  the  river.     Noti.e  the  ease 
"•-th  winch  the  particles  „,ove  about,  rise,  and  sink.     As  they  become 
<l".et,  shghtly  jar  the  vessel,  or  tap  it  with  tin-  end  of  a    HM,cil   am 
oUce  the  ease  with  which  disturbance  is  pnKluced  throu^l.:  a 
•l"..l.     Now  rap  the  si.le  of  the  block  with  a  hannner,  and  observe 
how  numovable  are  the  particles  of  wood.  ouscnc 

Our  experiments  teach  ns  that  the  molecules  of  solkh  are  not 
msily  moved  out  of  their  places;  conseqnentlv,  solid  masses 
form  such  a  frmly  connected  tohole  that  their  shape  is  vat  .asih. 
changed,  and  a  movement  of  one  part  causes  a  movement  of  the 
^rhole  On  the  other  hand,  the  molecules  of  liquids  have  scarcely 
any  fxcdness  of  position,  but  easily  slip  between  and  around  on^ 


20 


MATTKU    AND    ITS    PUOPMtTrKS. 


sclto  vossol,  a,Kl  arc  easily  separated  into  parts. 

,K,tatoos  are  ,k>,„c.,1  r,-o„,  haskot  t„  basket.     Wh   ,   im  i.llt 
II :«  lloiiml,  ,n,.kc«k-«  glide  past  o„e  another  '         '"' 

It  ,s  „ot  so  easy  to  stml.v  the  eharaeteristics  of  gases,  becaasc 
we  cannot  us„„l  ,■  see  then,.     ]!„t  we  nnu-  l,e  ai,le,I  I,    „   > 
Similar  to  that  en„„o,e.,  to  n.ake  the  „,o  veUlt ^f  ll^rWs^ 

or  h^ra=;-!frt ';:,■.::■  ":,:,""""■  r-r^'  -  ™»"  --" 
h.  the  path  or  the  .,«„.;.,:"„„  n  . r;:,':"'*!.,?! """'  "y"^ 

*^^,  and  freedom  oj  motion  amony  themselves  is  almost  perfect 
The,  appear  to  he  in  a  continual  state  of  repulsion,  aJlconZ 
<:nently  have  a  tendenc;,  to  expand  to  greater  and  grecUer  volumes 
li.cy  cxi,ancl  UKleflnitoiy,  unless  confined  by  pressure    while 
l",n.ds  and  solids  tend  to  preserve  a  unifonnlty  of  ^1^ 
I-.qu.ds  do  not  rise  al)ove  wl.at  is  called  thei.  surface,  and  we 

mte  s^crface   an.   there  is  no  such  thing  as  a  vessel  half  full  of 
MS.     On  the  other  hand,  if  gases  are  subjected  to  pressvre  their 

.^  ^"'^"^  ^^ssel  maybe  compressed  into  a  pint  vessel 

Pr  even  luto  less  space,  if  sufficient  forge  ia  u^cd.     m  ,om- 


THREE  STATES  OF  MATTER. 


21 


pression  of  liquids  is  barely  perceptible,  even  when  the  pressure 
is  very  great. 


§  17.  Philosophy  of  the  three  states  of  matter.  —  We 
conclude  from  the  difficulty  which  we  experience  in  separating 
the  parts  of  a  solid  body,  that  the  molecular  attractive  force  in 
solids  is  very  great.  From  the  ease  with  which  we  usually 
separate  the  parts  of  a  body  of  liquid,  we  might  conclude  that 
this  force  in  liquids  is  very  weak.  But  before  arriving  at  any 
conclusion,  it  is  necessary  to  consider  how  the  difficulty  of  sepa- 
ration of  the  parts  of  a  liquid  is  to  be  measured.  It  is  very 
easy  to  tear  off  a  portion  of  a  sheet  of  tinfoil,  but  we  should  not 
surely  regard  this  as  an  evidence  that  the  molecules  of  tin  have 
but  little  attraction  for  each  other,  for  in  tearing  such  a  body  we 
only  apply  the  force  to  a  comparatively  few  molecules  at  a  time. 
We  can  form  a  just  estimate  of  the  strength  of  molecular  attrac- 
tion only  by  attempting  to  separate  the  foil  into  two  portions  by 
such  means  as  that  the  separation  may  take  place  no  sooner  at 
one  point  than  at  another.  So,  too,  it  is  very  easy  to  separate 
a  drop  of  water  into  two  portions,  but  this  is  no  measure  of  the 
attractive  forces  unless  we  take  precautions  that  we  do  not  apply 
the  separating  force  successively  to  different  molecules.  If  we 
succeed  in  preventing  such  a  successive  action,  and  there  are 
certain  methods  of  doing  this  more  or  less  perfectly,  we  should 
find  the  process  much  more  difficult,  —  more  so,  indeed,  than  to 
produce  a  similar  change  in  many  solids.^ 

There  is,  however,  a  difference  in  the  molecular  action  in 
solids  and  liquids ;  such  that,  in  the  latter  state,  the  molecular 
forces  offer  no  resistance  to  a  shaping  force,  while  in  the  former 
state,  change  of  shape  can  only  be  brought  about  by  the  appli^ 
cation  of  considerable  force. 

In  a  gas,  on- the  contrary,  there  is  little  attranfion  between  the 
molecules ;  but  as  they  are  constantly  hitting  one  another,  and 
thereby  tendmg  to  drive  one  another  apart,  it  requires  an  external 
force  to  keep  them  together. 

» Tb*  wbwjv*  /or«?  pf  yrm )» dt  least  132  iba.  per  nt^me  Jncb,  -  Wajjwij*, 


22 


MATTER   AND  ITS   PROPERTIES. 


notlo,,  of  each  mole;uirh TkeZt"  f  1  *  "  '"""" '  '"  ""'"I"'  "■<= 
It  is  almost  or  quite  Impoii  1 ,  o  ?  "'""  '"  "  """^  "">«'>  wLc-ro 
urouncl,  aucl  ha^e  so^'ir,™  Cjlde 't'o"  «t""""  ^"  ''  "-"^  "■"' 

Practically,  the  condition  of  any  nortion  «f  m...     j 
"PC"   ite  tempeart„,-e  and  pressu/c/   Se"    §  Ls  >,    r"''" 
ordinary  pressures  water  is  a  solid  a  liodd  if  •■"  "' 

to  i^  ''■"Perature.so  anysnj;  „:'l'';;„r't:"""''""^ 

:r:ra[  t:;r "  ---  ■^  *-  oriXeriretr:: 

been  ohtainod  in  a  lin  nd  rff/  ,      "  ™1»">^<"'.  I'as  never 

"«.  ha,  neve  1^3c„  fd  tl^T^' '"'"""  ""«*""  '>«- 
"Ot  .,e  n,el,ed  unlLs  e  pre  rr  l^^^^^^^^^^^^^^^  "  ™'""-'  '""  ™"- 
•  entimeter.    For  a  similar  ™!!  ,  ^™""  '""■  *<1"»''° 

;-  -not  .eit.  •a^^'rz.Te  i!  rrt:;!:*,  r'-T 

l>cen    ji  )le    to  mwlimo    .    ♦  "-"^  >^<^'"s  iiuve  physicists 

a»^,LT*iflt:„rr:rT  »'."'-'^"  <«*™"  ->«'«"- 

and  nitr„„    "'"'^'•cnt  states,  there  is  great  diversity.     Ovv.ren 

errs  sfs  <"•,""■•-""'""  '^ "  ""•^""■''  <"•"■»  '"'- 
ti/o:,rwr  i::l:  ,:r:^:r^^ 

nressnre     On  the  other  hand,  certairsl:^,  'L      r™';:,: 

»»%  „„  „»  lemp„-„,ure  ami  p,;,,,,„;. :  „„  ,,,,„,  „„„,,  !!'J  .*^™* 
.egurded  as  sin„.,v  n„.t,.r  in  a  IV„«.n  state",  eve';  i,:  i  ^riT 
tcr  ,„  a  n,elte.d  state,  and  eveiy  gas  as  n.atter  in  ■I.ZttT^^, 


t>iiENOMENA  OF  ATT  H ACTION". 


Kvery  liquitl  has  been  solidided  and  volatilized,  and  every  gas 
has  been  liquefiptl  and  soliditied.  Air  was  one  of  the  last  of  tlie 
gases  to  surrender  its  reputation  of  being  a  "  perujanent  gas." 
Not  till  the  year  1878  was  it  reduced  to  hunps.  We  may  predict 
the  future  of  our  globe.  If  its  heat  increases  sufficiently,  the 
whole  world  will  become  a  thin  gas.  If  its  heat  diminishes  indefi- 
nitely, all  earth  and  air  will  become  a  solid  mass. 

III.  PHENOMENA  OP  ATTRACTION. 
According  to  the  circumstances  under  which  attraction  acts, 
we  have  the  various  phenomena  called  gravitation,  cohesion,  ad- 
hesion, capillarity,  chemism,  and  magnetism.  Sometimes  these 
terms  are  used  as  names  of  the  unknown  forces  that  cause  the 
phenomena. 

§  la  Gravitation.  — Thnt  attraction  which  is  exerted  on  all 
matter,  at  all  distances,  is  called  gravitation.  Gravitation  is 
universal,  that  is,  every  molecule  of  matter  attracts  every  other 
molecule  of  matter  in  the  universe.  The  whole  force  with 
which  two  bodies  attract  one  another  is  the  sum  of  the  attrac- 
tions  of  their  molecules,  and  depends  upon  the  number  of  mole- 
cules the  two  bodies  collectively  contain,  and  the  mass  of  each 
molecule.  Tiie  whole  attraction  between  an  apple  and  the  eartli 
is  equal  to  tlie  sum  of  the  attractions  between  every  molecule 
in  the  api)le  and  every  molecule  in  the  ear*h. 

§  19.  Weight.  —  It  is  scarcely  necessary  to  state,  that  what 
U  understood  by  the  weight  of  a  body  is  the  mutual  attraction 
l)etween  it  and  the  earth.  The  term  mass  is  e(iuivalent  to  the 
expression  quantity  of  matter.  It  follows,  then,  that  weight  ia 
proportional  to  mass.  Why  do  we  weigh  articles  of  trade,  such 
as  sugar  and  tea? 

§  20.  Does  the  apple  attract  the  earth  with  as  much 
lorce  t*i=  TJno  caiou  auoritcis  tne  apple v  —  i.i-L  us »-xiiiiiiiie this 
question.  First  assume  M.at  tlic  nioleeulos  of  tlie  apple  and  tlie  eartlj 
have  equal  masses,  i.e.,  are  horaogeueous;  tlien  tlie  attraction  of  any 


%\ 


24 


MATTER  AND  ITS   PROPERTIES. 


i 

'r 


M    I 


molecule  in  the  apple  for  any  molecule  in  the  earth  is  Pn„ni  i     .u 
attraction  of  any  molecule  in  the  earth  for  any  moCle  inTh  }" 

That  J  ,,,,  ,,,,,  ^„,  ^,,^  ^^^^^  ^^^^^^^^^  eLh  o  a  Igle  i^ke  r: 
cule,  their  attract  on  for  each  other  wnniH  ).„  i    ^      *  °'®" 

.he  .pp,eco„..i„,.„„.„^7i'e:i';:;;ri:rrc„,!:"'v7rr''"' 

w,.h  Which  one  molecule  ...ract,  a„„.|,er  be  rpreseMed  t  '  r° 
each  molecule  of  the  anule  atlracf,  tl,.  «.  "'',*'"■"'  "^  »■  Now 
with  a  force  of  5  „  .  tTi^ ,   "       ,  '"  """''"l"'  1"  the  earth 

the  eartK  with  a  f:;ce  ofTo  „  Ou™  ^l  "" ,  "■»'"'>■ '-vouid  «.tr«,t 
of  the  earth  attract,  the  moLu        of  t  faUriira  T'""'^ 

soniu«  Will  i^;i;j^z  tZio'tt.^  r;:f  7- 

whose  masses  diBTor,  „„d  consequently  between  rjr,  T    u"!' 

rs-r,:  ;t^r:f  ,r-rl"  --t  ""'•"'  -" 

the  former?  ^         ''  "'  '*'""^'^  **^  ".e  latter  attracts 

If  the  apple  attracts  the  earth  as  stronjriv  no  +i.„ 

«» .  Ship.  His  purr<-™r  tiT.;'.:  r:?  huVthrrr,'"" 

not  appear  to  move.    But  if  flve  hunrlrerl  m„n  ^'^  ''''*'^ 

together,  the  ship  would  be  ."oln  to  mfvo  Dill  Z^'  ''''^'  '''''''' 
motion?  If  so,  then  would  the  fl^e  hundred  men  nrodn:;  '^  '"  '" 
since  five  hundred  times  nothing  is  nothing?  '^    ''"''  "^  '"°"""' 

You  will  learn,  in  the  next  chapter   tliaf  u.n  =..„      ., 
a  given  force  moves  a  hody  in  a    'J  ^t  1    "'^'^^^.'^  ""-o-'fe-h  which 

the  mass  of  the  body.     Does   IL  f^ctlT"  T"'  '"'"'''^y  *« 
nomena?  ^  "'   ^"''  '^P'*''"   "'e   foregoing  phe-      . 

from'; J^n^rOb^^^^^  .-^*^  *^«   <^i«tance 

^"- the  force  of  ,ravit,  ^: t":;:::?:::^;:''^ 

the  greater  is  the  force  o^rlvt       tI  e    ^"''^  ''  ""  ^"^^" 
earth  IS  about  26  miles  less  thnn  ifc  I    .".  " '^'  "'  '^'*^ 


PHENOMENA  OF  ATTIIACTION. 


25 


poles  is  13  miles  less  than  to  the  surface  at  the  eqnator.  This 
considerable  difference  in  distance  from  the  center  oc(!asions  an 
appreciable  difference  between  the  weight  of  a  body  (having  any 
considerable  mass)  at  the  equator  and  at  the  poles;  and, "since 
the  distance  of  the  surface  from  the  center  constantly  increases 
as  we  go  from  the  poles  toward  the  equator,  the  weight  of  all 
objects  transported  from  the  poles  toward  the  equator  constantly 
diminishes. 

.  It  is  obvious  that  any  object  raised  above  the  eartli's  surface, 
as  in  a  balloon,  must  weigh  less  than  at  the  surface  of  the  earth.' 
But  the  bights  with  which  we  commonly  have  to  deal  in  our  ex- 
periments are  so  small  in  comparison  with  tlie  earth's  ividius,  that 
the  differences  in  weight  due  to  diircrencos  in  bight  at  a  given 
place  can  scarcely  be  detected  by  most  delicate  t(>sts. 

The  statement  that  "  weight  is  proportional  to  mass"  (§19) 
must,  therefore,  be  restricted  to  a  comparison  of  masses  at  the 
same  place  and  at  the  same  aUitiide  only.  The  pi-opriety  of 
making  a  distinction  between  the  terms'  mass  and  weif/ht  is 
now  apparent,  as  the  former  impHes  tliat  which  does  not  ciiange 
when  a  body  is  translerred  IVom  place  to  place,  while  the 
latter  ma3-  change. 

If  the  earth  were  of  uniform  density,  bodies  carried  below  its 
siuface  would  lose  in  weight  as  the  distance  below  the  surface 
increases.  At  one-fourth  the  distance  to  the  center  there  would 
bo  a  loss  of  one-fourtii  the  weigiit.  At  one-half  the  distance 
the  weight  would  be  one-iialf;  and  at  the  center  nothing.  Is 
weight  an  essential  property  of  matter  ?  State  certain  condi- 
tions on  which  a  body  would  have  no  weight. 

The  terms  up  and  down  are  derived  from  the  attraction  be- 
tween  the  earth  and  terrestrial  objects.  J)own  is  toward  the 
center  of  the  earth,  or  it  is  the  direction  in  which  a  I)odv  <alls  or 
tends  to  move  in  consequence  of  gravitation.  Up  is  the  opi)o- 
site  direction.  It  is  apparent  that  the  up  and  down  of  one 
place  cannot  correspond  with  the  up  and  down  of  any  other 
place. 


^J6 


MATTER  AND  ITS   PROPERTIES. 


QUESTIONS. 

must  y„„  tun,  yo„r  face  In  order  to  look  "p  ?  '"'"°" 

the,  „„tl,  look  i/tho  Ze  ZS;,         "    "'■  °'  ""  "'"■"'•     """"^ 

e.   What  is  the  ori^Mu  of  "  water-power"  ? 
<•    vv  hat  IS  the  cause  of  tides? 

wefu:.";:"/!";™:::;";'"' "'° "™  "'>"'- «-"'«» 3-  wo,,,, 
haiate.'irt  e :  aL°''or«:r;:r''''  °'-"'""  "■"""" """  -p*s- 


'    'I 


t       i 


§  22.  Cohesion. -That  attraction  which  holds  the  molecules 
of  the  same  substance  together,  so  as  to  form  larger  Tc  i^  is 
ealled  cohesion.     It  is  the  fornn  fi,of  .  ooaits,  13 

all  bodies   from  f.  11  prevents  our  bodies,  and 

.  au  oouies,  Horn  falhng  down  into  a  mass  of  dust      T^  Ja  fi   4. 
force  »^,ie„,.o,i3t,  u  fo,.ce  te„di„«  to  b,.e„k  or d,  'a  ,  .^    " 


CRYSTALLINE   CONDITIONSOF  MATTER.  27 

fluid  condition,   then,  bv  nrp«j<5iiro    tu^        i 

tie,  VISCOUS,  malleable,  ductile,  and  tenacious  ' 

§23.  Crystalline  and  amorphous  conditions  of  matter 
-If  our  v.s,on  conkl  be  rendered  keen  enc.^b  to  enib^.   T* 

u..ox„lo,„,  „„,,<,,  tl,o,.o  „„l„„  nndouh     „      ;  tS  ;    ' 
wonders  .and  be.intios  of  wi.;,  i.         i  untoided  to  us 

tlie  same  substaiiue),  we  ijet,  i)os8i,,lv  U- ,,:«■  *      ' 

and  b,il,iant  diamond  iu  l,,„  „„e  cjctb^ft         '  '''"""^'■""- 

>ooM„g  graphic  i„  .„„„.„.,  a^iT-u^t  f,;„r;';',:r'''"; 

shapeless  ehareoal  poious,  Dlaek,  and 

jou  get  rough  and   "^d  smtcl      T  °"'"  *"'=''°"' ""'' 


I 


28 


MATTKU    ASt)   JTH    flU,l'FAmm. 


m 


of  elium,„|.  '  «''"'  «'"""  "'"'  '-"'l-'X  i"  tlic  luim 

wal..r;  HUsp.nU  .  u,    I  n^t^:^  '"'';' '''''    '"-"^"  ">  ^O^-"  of  hot 

"""""'« '"••  -' -  ^' ' .,  '^'z:xz:iZ;:r '''''"'  '"■^' 

"I-   »»ll|"lr.'.     All,,,!    Il„.    n„„,V,     '""■.»■'••)"'  »"ril»,T ,lrhl,„.i,|„ 

»-ii.i„.,  wi.,a,,,,,,;:';,,,i^r/;,  ::;■;;*,-■' /•  '■'■  "•  «■« 

y<)ijr..yi;„;,  "  "^^ '« '^  "'«>■>«  «(,ii,g  ou  before 

""I  .v""  "viii  I ,,,„.  „„rr,.,...  m„C  „,..?,  'r' "  "'"""■■'«"■• 

>',  wuuoii.  „„ui„,  „„.  .„„,  „^:.,„„.,i  ,t:t;,r"K::' ';;:: 


of 
iiK 


est 


Riippi 
from 
incre 
we  fii 
by  cc 


OHAXGE  OF    VULUMIO   15V   CUVSTALLIZATION.  29 

ofico  fs  a  mass  of  crystals,  so  closely  packed  together  that  the 
individuals  are  not  distinguishal)lo. 

§  24  Change  of  voltime  by  crystallization.  -  This  tend- 
ency of  matter  to  structural  arranooment  is  not  only  very  inter- 
esting, but  very  important  in  the  arts.     It  is  very  natural  to 

Fig.  10. 


snppose  that  the  new  arrangement  of  molecules,  when  nassina 
Iron,   tlie  ii(,ui<l   to  the  .solul   state,   should   <,cc..sion   ni'her   ,1 

increase  or  diminution  in  vol We  are  not  surprised  when' 

we  find  that  water,  in  freeziug,  disregards  the  law  of  c.-ntraction 
by  cold,  and  that  the  molecules  are  not  found  so  closely  packed 


*  '• 


*t| 


so 


Matter  and  its  WiopEHTifia. 


m 


"li  1 


ii    ' 


togethor,  in  the  now  and  strac-tural  state,  as  when  under  th. 
inHnenoc  of  cohesion  alone.  ™ 

The  force  exerte.l  by  tlie  molecnies  in  clmnein.  nosition,  :, 
so  e„om,ons  as  to  hnrst  the  stronges't  vessels.     Hence  ote 

ee.p„K.s  a,-e  h.n-st  when  water  is  .allowed  to  free.r  1"^  ,  ' 
Huge  rocks  arc  dislo,lgod  from  their  restin<..nlaces  rthr,,  , 

s;" "■» ■"™'"'^'"-*'^ "3- "'er getti^^'ii : .;:  7 

ee^,  g,  expanding  year  after  year,  and  pushing  the  ^1,3 
Horn  then-  support.     Cast-iron  and  many  allovs  „fcbT.  . 
met.,,,  expand  o„  .soli.liiying.     ,s,„„  Jeu'^^'t    a  f ^ 

t  e  mold.    Most  uietals  oontmct  on  solidifving.     Hence  ..old 

that  the  ™„,eeu,cs  of  iron,  whe,.  sl,:i.«:^p":  i  tl/e  jZ™    a  ! 
free  to  arrange  themselves  in  their  peculiar  Lth«^^  'Z  t  St    , 
this  new  arrangement,  the  cohesive  force  is  weakened. 

§25.  What  18  the  cause  of  this  almost  universal  t.„ 

denoy  of  matter  to  orystaUize?      w„   1    ""™™»' "n- 

knowledge  of  the  doinmTr^       .      ,  ™    "°   "^""''"^ 

B^       lue  noings  m  tlie  molecular  world      Rut  „.«  i.„ 

»«spe.,U  each  needle  bv  0  .br;..^.,     hT  t       ]°  H   T"*'""'    "'"' 
burlzontal  position.    Brine  the  „„    ,r  °  b«l»iice<l  In  a 

other.  Brin.  the  „«,e^  r„:r„:4  z  :,r i/t:  r: 


^1 


HARDNESS. 


3] 


Bring  the  point  of  one  near  the  point  of  the  other.     Brintj  the  eve  of 
one  near  the  eye  of  the  other.     What  is  the  result  in  each  case?    Til 

ITX.  '''  '''''''  "''  '""'  °'  "''  "'''"'  '^^'''^'  ""''  '''''  '^^ 

Now.  break  one  of  the  needles  into  two  pieces,  and  experiment  as 
before.  Break  U.em  into  still  smaller  pieces,  and  the  smu  J  Lee 
that  you  can  obtain  possesses  polarity,  as  certainly  as  the  ori  i  ,al 
needle       nnvgine  the  work  of  division  to  be  continued  till  t      mole'    1 

poSyT  ""''  '°  "^""^  ""*  ""  ^"«^-"^«  --^y  P--e- 

Throw  a  dozen  of  these  magnetized  needles  on  a  sheet  of  paper  and 

r Xhr  tv""  tT  "'  ?%'"""^  "^'""^^^^^^^  ^''^  -^  appLra"  e  ;' 
legulanty?  If  two  arc  to  forma  rigid  group,  how  must  they  be  ar 
ranged?    How  is  it  with  a  group  of  three? 

Experiment  2.  Next  place  a  magnet  beneath  a  sheet  of  paper  and 
s.ft  ,ron  l^hngs  over  it.  Gently  tap  the  paper.  This  renunds  us  o'f  the 
effect  of  jarr,ng  on  the  car-axle  and  cannon,  where  molecules,  once  set 
in  .not.on,  tend  to  arrange  themselves  according  to  some  guiding  prh, 

th'nrai;"  it'  '  ""  ""'""'  "'  '  '''  "'  """  """^'^'^  ^-^  §  ^««).  -d 
We  pass  readily  from  these  facts  to  conclusions  respecting  the  mo- 
ecular  arrangement  in  the  crystal.  Only  grant  the  supposition  that 
the  molecule  .s  endowed  witii  something  similar  to  polarity,  and  we  • 
can  picture  to  ourselves  the  molecules,  like  the  iron  fllings.  wheelin' 
into  Ime  in  obedience  to  their  polar  forces.  Crystals  are  more  easilj 
cleft  m  some  dn-ecfons  than  in  others;  n.ay  not  this  be  accounted  for 
by  supposmg  that,  like  the  magnet,  the  attraction  on  some  sides  of  the 
molecule  is  greater  than  on  others? 

§  21.  Hardness. -Name  some  metal  that  you  can  scratch 
with  a  finger-nail.  See  if  you  can  scratch  a  piece  of  copper 
with  a  piece  of  lead,  and  vice  versa.  Get  as  many  specimens  as 
possible  of  the  following  substances  :  talc,  chalk,  glass,  quartz 
iron,  silver,  lead,  copper,  rock-salt,  and  marble.  Ascertain 
whu.b  of  them  will  scnrtch  glass,  and  which  are  scratched  by 
glass.  What  term  do  we  employ  in  speaking  of  those  substances 
that  are  easily  scratched  ?  To  those  that  are  scratched  with 
difficulty.?     Which  is  the  softest  metal  that  you  have  tried' 


.)  d 


hi 


MATTRIl    AND   ITS   riiOPERTIES. 


Ihoh^dst:     Whi.hs  the  softer  .etal,lr.n  or  load?     Which 
W^  ":  r '"  ■      '''^^  "^'•'''"-  ^M.end  upon  don^^ 

When  vv.ll  ,,1,0  sMbstu.K-o  sctitch  a.iothor? 

io  onahlo  MS  to  express  ,h.o,,>c.s  of.  hardness,  the  followhicr 
*uble  ol  reference  is  generally-  adoi^ted  :  _  "^ 

MOIIIfS  SCALE  OF  HARDNESS. 


1.  Talc. 

2.  Gypsum  (or  Rock-Salt). 
^.  Calcite. 
4.  Fluor-Spar. 
5-  Apatite. 


■< 


fi.  Ortlioclase  (Feldspar). 

7.  Quartz. 

8.  Topaz. 

9-  Conindiitn. 

10.  Duunoud. 


o„e  or  «,„  n^..i::  r;rt::  ;L:-^-';r«:' ,::;r";?  ^ 


Fiff.  11. 


§27.  Flexibility. -Such  substances  as  may  be  bent  or  admit 
of  a  huige-hlve  movement  among  their 
molecules,  are  calhdjlexiljle.  AVhat 
difrerence  have  you  noticed  in  differ- 
ent jack-knife  blades ?  How  can  ^on 
tell  a  soft  blade  from  a  hard  ])lade^ 

molc^ulcr^ntlof''  "-J"  '''^""  ^^'  '^  ^^  ^^^P^-"^  ^hat  the 
r  tHe  f?r  ..^''''' "^'  "i"«t  be  separated  from  each  other 
a  httle  farther  than  usual,  and  that  they  must  Inve  su2Z 


ELASTICITY. 


88 


iron,  zmc,  and  lead.  Stretch  the  piece  of  rubber.  What  change 
la  Its  molecular  condition  must  occur  when  it  is  stretched? 
What  molecular  force  causes  it  to  contract  when  the  stretching 
force  18  removed?  Compress  the  rubber.  What  chancre  of 
molecular  condition  takes  place  in  compression?  What^foroe 
causes  it  to  expand  when  the  pressure  is  removed?  Bend  eacli 
one  of  the  above  strips.  Note  which  completely  unbends  when 
the  force  is  removed.  Arrange  the  names  of  these  substances 
•n  the  order  of  the  rapidity  and  completeness  with  which  they 
unbend.  *' 

What  change  takes  place  among  the  molecules  on  the  concave 
side  of  the  bent  strips?    What,  among  the  molecules  on  the 
convex  side?    What  two  forces  are  concerned  in  the  unbendin<.? 
Twist  the  cord  of  a  window-tassel.     What  causes  it  to  untwist' 
Ihe  property  which  matter  possesses  of  recovering  its  former 
shape  and  volume,  after  having  yielded  to  some  force,  is  called 
elasticity.     To  what  forces   is  elasticity  due?    Does  all  mat- 
ter possess  this  property  in  the  same  degi-ec?    Does  the  rub- 
ber  possess  the  same  ability  to  unbend,  as  to  contract  after 
being  stretched?    In  what  four  ways  have  you 
tested  the  elasticity  of  substances  ?    Does  a  sub- 
stance possess  equal  power  of  recovering  its  form 
aft«r  yielding  to  each  of  these  four  methods  of 
applying  force?    Why  are  pens  made  of  steel? 
What  moves  the  machinery  of  a  watch?    What 
is  the  cause  of  the  softness  of  a  hair  mattress  or 
feather-bed  ? 

A  common  spriug-balance  used  for  weighing  con- 
sists of  a  steel  spring  wound  into  a  coil.  The  weight 
of  the  body  to  be  weighed  straightens  or  draws  out 

AX    A  A.  .  ,       *^'''"^"     ^  1'°'"*^''  moving  over  a  plate  which  is 

divided  into  equal  parts  shows  how  much  the  sprint  ha-  h-n  ^-a-n 
out  But  the  entire  virtue  of  this  apparatus  consists  in  the  elastlcliy 
of  the  spring,  or  its  power  to  recover  its  original  form  after  bein- 
drawn  out.  Give  other  illustrations  of  the  application  of  elasticity 
to  practical  purposes. 


Fig.  12. 


•31 


I 


84 


MATTER   AND   ITS   PROPERTIES. 


;  "■ 


n 


Any  alteration  m  the  form  of  a  body  due  to  the  application  of 

.lodl h'-'  n  ;\'''''"'"'  ""^^  *''^  '''''''  "^y  ^'"^''^  ^'««  strain  i.s 
produced  ,s  called  the  stress.  A  body  which,  having  experienced 
a  strani  due  to  a  certain  stress,  completely  recovers  its  original 
conchtion  when  the  stress  is  removed,  is  said  to  be  perfectly 
elastic.  Liquids  and  gases  are  perfectly  clastic  (see  §  48) .  Solids 
arc  perfectly  elastic  up  to  a  certain  limit,  which  varies  greatly  in 

tl7^T  1":T'  ''  ""  ^'"^^  '""'''^^  ^  certain  nmii,\he 
foim  of  the  solid  becomes  permanently  altered,  and  the  state  of 
the  body  when  the  permanent  alteration  is  about  to  take  place, 
8  called  the  hnut  of  perfect  elasticity.  In  sof^  or  plastic  Llies 
tins  unit  ,s  soon  reached.  ,  What  is  the  result  of  overloading 
carnage  springs  ?  * 

.n^i^^H"**^^^^^-"^'''''^'  '^'^'^'  ''^""'^  ^'th  a  hammer  to 
each  of  the  substances  whose  hardness  you  have  tested  (§  26) 
and  ascertain  which  are  the  most  easily  broken  or  pulverized.' 
Obse.ve  that  some  substances  suffer  a  permanent  change  in  form 
when  subjected  to  a  stress  which  exceeds  their  limit  of  elasticity, 
while  others  break  before  there  is  any  pcrmaiuut  alteration  in 
lorm.     Ihe  latter  are  said  to  be  brittle. 

J  30.  Viscosity. -Support  in  a  horizontal  position,  ar  one 
of  Its  extremities,  a  stick  of  sealing-wax,  au.l  suspend  i'romits 
nee  extremity  a  small  weight,  and  let  it  remain  in  this  condition 
several  days,  or  perhaps  weeks.  At  the  end  of  the  time  the 
stick  will  be  found  i)ermanently  bent.  Had  an  attempt  l,een 
n.u  e  to  bend  the  stick  quickly,  it  would  have  been  found  qi.ite 
little.  A  body  which,  subjected  to  a  stress  for  a  considerable 
^me  suffers  a  permanent  change  in  form,  is  said  to  be  viscous. 
Hardness  ,s  not  opposed  to  viscosity.  A  lump  of  pitch  may  be 
quite  hard,  and  yet  in  the  course  of  time  it  wiU  flatten  itself  out 

Oy  Its  own  weiffht,  jind    fl«w   /1„..,.,    k;i!   i:'— 

ij     .,    ,.,         ':    '   '■"''  '»"  *"iy  a  scitaiii  of  syrup. 

I;.qu.d8  like  molasses  and  honey  are  said  to  be  viscous,  in  djs. 
tinction  from  limpid  liquids  like  water  and  alcohol. 


TILNACITV. 


S5 


§31.   Malleability  and  ductility.  -  Some  stibstanoos  pos- 
sess, in  tlie  solid  state,  a  <rrtain  a.noni.t  oi' flauUt,! ;  that  is, 
tlieir  molecules  may  be  displaced  without  overcominjr"  their  oohe- 
sion.     Place  a  piece  of  lead  on  an  anvil,  and  hammer  it      Jt 
spreads  ont  nnder  the  hammer  into  sheets,  witiiont  being  broken 
though  .t  is  evident  that  the  molecules  have  moved  about  amon^^ 
oiie  another,  and  assumed  entirely  different  relative  positions" 
Heat  a  piece  of  sort  glass  tube  in  a  gas-flame,  and,  although  the 
glass  does  not  become  a  liquid,  it  behaves  very  much  like  a 
liquid,  and  can  be  drawn  out  into  very  fine  threads.     When  a 
solid  possesses  sunicient  flui<lity  to  admit  of  being  drawn  out 
into  threads,  it  is  said  to  be  dmtik.^     When  it  will  admit  of 
being  hammered  or  rolled  into  sheets,  it  is  said  to  be  malleable. 

iJ^  ""n"!  'I?  '^»''^*"^''  '^'"'  substances  thai  are  dnctile  are  also  mat- 
leable.  But  the  same  suljstance  does  not  usually  possess  tlie  two 
properties  in  an  equal  degree.  Platinum  is  the  u,ost  ductile  metal.  It 
can  be  drawn  into  wire  finer  than  a  spider's  tln.ad.  It  is  the  seventh 
metal  ,u  the  rank  of  malleal.ility.  Goi  ,  the  most  malleable  metal. 
It  can  be  hammered  into  leaves  so  tuin,  that  it  would  require  300  000 
o  make  a  book  one  inch  thiek.  It  nu.ks  next  to  platinum  in  ductufy 
I.ou   at  a  red  heat,  is  very  malleable  and  ductile.     What  metals  can 

sheetTr'        '""''^    ^^'''  "'''''^'  '*°  ^"^  •■""'^'  ""'  hammered  lute 


ti^l 


.  .§  32.  Tenacity.  — Tn  order  that  a  substance  may  be  ductile, 

Jtis  evident  that  it  nmst  possess  a  strong  cohesive  force,  so  as 

ft^p^event  rupture.    The  power  that  matter  possesses  of  resisting 

^^ra|)tiifre,,l)y;a4)uiling  ftM-ce,  is  called  tenacity.''    A  body  may  C 

gemeious^tkout  being- Aiktile,  but  it  cannot  be  dnctile  ivithom 

mmg  mhcions.     It  is  remarkable  that  the   tenacity  of  most 

metals  is  increased  by  being  drawn  out  into  wires.     It  would 

seem,  that,  in  the  new  an-angement  which  the  molecules  assume, 

the^cohesive  force  is  stronger  than  in  the  old.     Hence  cables 

made  of  iron  wire  twisted   together,  so   as  to    form  an   iron 

'  Ductile,  draw-able.  ,  Malleable,  as  1{  were  malltt-abU. 

» Tenacity,  properly  of  holding. 


I  ' 


Is"! 
t.'l 


|!    a 


86 


MATTER  AND  ITS   PROPERTIES. 


rope,  are  stronger  than  iron  chains  of  equal  weiglit  and  length, 
and  are  much  used  instead  of  chains,  where  great  strength  is 
required.  ^ 

§33.  Adhesion.— Grasp  with  your  finger  a  piece  of  gold- 
leaf,  and,  honest  as  you  may  be,  it  will  stick  to  your  fingers ;  it 
will  not  droi)  off,  it  cannot  be  shaken  oflT,  and  to  attempt  to  pull 
it  off  IS  to  increase  the  difficulty.  Dust  and  dirt  stick  to  clothing. 
Thrust  your  hand  into  water,  and  it  comes  out  wet.  You  can 
climb  a  pole,  because  your  hands  stick  to  tlie  pole ;  but  if  the 
I)ole  is  greased,  climbing  is  not  so  easy.  We  could  not  pick 
anythmg  up,  or  liold  anything  in  our  hands,  were  it  not  that 
these  things  stick  to  tiic  hands. 

Every  minute's  experience  teaches  us  tliat  not  only  is  there  an 
attractive  force  between  molecules  of  the  same  kind  of  matter 
but  there  is  also  an  attractive  force  between  molecules  of  unlike 
matter.  That  force  which  causes  unlike  substances  to  clin^r 
together,  is  called  adhesion.  Is  adhesion  a  molar  or  a  moleculaT- 
force?  How  does  it  differ  from  cohesion?  Wliy  do  not  gold 
watches,  and  other  articles  of  gold  jewelry,  appear  to  stick  to 
tlie  fingei-s?  Wiiat  keeps  nails, driven  into  wood,  in  their  places? 
What  would  happen  if  all  adhesion  between  tlie  different  parts 
of  the  building  you  are  in  should 
be  suddenly  destroyed?    When  a  *''^- '^• 

liquid  sticks  to  a  solid,  what  term 
do  we  usually  employ  in  describ- 
ing the  phenomenon? 


Experiment  1.  Shake  a  small 
quantity  of  olive-oil  In  water,  and  ob- 
serve the  form  assumed  by  the  frag- 
ments of  oil  as  they  rise  throiigli  the 
water.  Does  this  experiment  indicate  that  the  adhesion  between  the  oil 
and  water  or  the  cohesion  in  the  oil  is  the  stronger  ? 

s-  --  >-._.j!.i!!.  „  p.atc  ot  giuss,  about  «»=">  scmare.  from 

one  arm  of  a  scale-beam,  attaching  the  threads  to  the^plate  with  seallZ 
wax.     Balance  it,  and  place  a  dish  of  water  under  the  glass,  so  thati?« 


CAPILLARITY. 


a7 


tinder  surfac.  will  jnst  touch  the  surface  of  the  water  Add  small 
we  ghtuntilthe  glass  leaves  the  water.  Kxan.ine  the  unc.-^  of  t  " 
glass.  Have  you  separated  the  j^lass  from  the  water,  or  have  you  torn 
the  water  apart?  Do  you  inf,.r  from  your  experiment  tMt^hlnT 
h^^r.  ^een  the  ,lass  and  the  water,  ^r  the  c^rLr  ^^Lm!; 


Is  there 


Glass  is  wee  >y  water,  but  is  not  we     )y  mereurv. 
no  adhesion  bacween  morctiry  and  glass 

E.peri.„e«t  2  Substitute  .nercury  for  water  in  the  last  expori- 
ment  Do  yor.  Hnd  any  indication  of  adhesion?  Is  it  j^reater  or  less 
than  that  between  glass  and  water?  ^ 

It  is  probable  that  there,  is  some  adhesion  hetioeen  all  cuhstanees 
when  brought  in  contact.  If  a  liquid  adheres  to  a  solid  more 
firmly  than  the  molecules  cf  the  liquid  cohere,  then  loill  the  solid 
be  wee  by  the  liquid.  If  a  .solid  is  not  wet  bv  a  liquid,  it  is  not 
because  adhesion  is  wanting,  but  because  ooliesion  in  tlie  liquid 
IS  stronger.  That  gases  adhere  to  solids  is  proved  by  the 
phenomena  of  absorption  desci-ibed  in  §  37. 

QUESTIONS. 

1.  Why  will  not  water  wet  articles  that  have  been  greased  ? 

2.  Why  is  it  difficult  to  lift  a  Ijo.ird  out  of  wat.T  ? 

8    Why  does  water  run  down  the  side  of  a  t.nnhlor  when  it  is 

venti'g'lt   "         "'  '•"""'  """""^  '    '"-'"^^  •'^'""•'  -'"">''  "^  P- 
4.  In  what  does  the  value  of  cement,  glue,  an.l  mnrilair.  consist  ? 
6.   What  enables  you  to  leave  a  mark  with  a  pencil  or  crayon  ? 

§  34.  Capillarity.  —  Examine  the  surface  of  water  in  a  goblet 
^ou  Hnd  the  surface  level,  as  in  \  (Fig.  14),  except  aroun.l  the 
edge  next  the  glass,  wiiere  the  water  is  curved  upward  so  as 
to  resemble  the  interior  surface  of  a  watch  crystal.  Mercury 
placed  in  a  goblet  (B)  has  its  edge  turned  downward.  rcso,nb!in.r 
the  exterior  surface  of  a  watch  e.,..aK     This  seems  to  indicate 


r.  1 


m 


Matter  and  its  pRoPEUTiEd. 


a  repulsion  between  mercury  and  glass.  But  a  previous  e^peri- 
nent  (i^ge  37)  has  shown  that,  instead  of  repulsion,  thereTs  . 
slight  adhesion  between 


Fig.  14. 


these  substances 

Pour  any  liquid  on  a 

level    surface    wiiich   it 

does   not   wet,  —  e.  q., 

water    on    parafline   or 

wax,    or    mercury    on 

glass.    It  s[)reads  itself 

over  the  surfiice,  but  the 

edges    are    everywhere  ^ 

rounded  or  turned  down  ^ 

like  the  edges  of  mercury  in  a  goblet.     Surely  those  romulcl 

edges  are  not  caused  by  the  repulsion  of  the  sides  of  a  v 

The  edges  of  all  liquids  will  be  turned  down  unless  the  adhes  on 

between  the.n  and  the  sides  of  the  vessels  exceeds  the  cole  io 

I"  the  hquul      The  glass  does  not  cause  the  turning  down  o 

prevelitT       '""''"'^'  "'  "'"  ^''^''''  ~ '''  '""^""'^'  ^^  '■^^''"-  ^« 
Thrust  vertically  two  plates  of  glass  into  water,  and  gradu- 
all3  brmg  the  surfaces  near  each  other.     Soon  the  water  rises 
between  ^o  plates,  and  rises  higher  as  the  plates  are  brought 
nearer.     Thrust  a  glass  tui,e  of  very  fine  bore  into  water;  the 
a  traction  w,t lun  it,  on  all  sides,  will  raise  the  water  to  twice  the 
lugh    ,t  would  reach  when  between  two  plates  whose  distance 
apart  ,s  equal  to  the  diameter  of  the  bore  of  the  tube.     Thrust 
a  tube  of  the  same  bore  into  alcohol ;   this  liquid  rises  in  the 
t..be,  but  not  so  high  as  water.     The  surfaces  of  both  the 
Water  nn.l   the   alcohol   are   concave.     If  the   tube   is   placed 
in  mercury,  the  opposite    phenomena    occm- :    the    mercurv  is 
depressed,  and   its   surface   is  convex.i     Both  ascension  nnd 

'The   SCODC   Oi'   Uil«    Jmnk   "'M!    r\r.t    a-l-n!'    -f  1 

o.pl]I„I„.    The  .■ud.M  ,™  „„V.  1,°,:  J   ;  °  LlTt  "'""":""»  ,"'  ■I"'  Pta.o,.™„  „, 


CAPILLARITY. 


39 


depression  dimiuish  as  the  temperature  increases,  being  greatest 
at  tlie  freezing  point  of  the  given  liquid,  and  least  at  its  boiiin^ 
point.  (Regarding  heat  as  a  repellent  force,  can  you  give  any 
reason  wliy  the  ascension  should  be  less  at  high  than  at  low 
tcn,perat.n-cs?)  Inasmuch  as  the  phenomena  are  best  shown 
in  tubes  having  bores  of  the  size  of  hairs,  they  are  in  such 
cases  called  capillary'  phenomena,  and  the  tubes  are  called 
capillary  tubes.  ^ 

The  phenomena  of  capillary  action  are  well  shown  by  placing 
FJ815.  various  liquids  in  U-shaped   glass 

tubes,  having  one  arm  reduced  to  a 
capillary  size,  as  A  and  B  in  Figure 
15.   Mercury  poured  into  A  assumes 
convex  surfaces  in  both  arms,  but 
does  not  rise  so  high  i'    the  small 
arm  as  it  stands  in  the  large  arm. 
Pour  water  into  B,  and  all  the  i)hc- 
nomona  are  reversed.     C  is  a  glass 
tube  containing  water  and  mercury, 
and  showing  the  shapes  that  the  surfaces  of  the  two  liquids  take. 
Generalizing  the  above  facts,  we  have  the /owr  laws  of  capil- 
lary action :  — 

Liqnifh  rise  in  tubes  when  they  ivet  them,  and  are  depressed 
when  they  do  not. 

The  ascension  or  depression  varies  inversely  as^  the  diameter 

of  the  bore.   • 
The  ascension  and  depression  vary  ivith  ^  the  nature  of  the 

substances  employed,. 

The  ascension  or  depression  varies  inversely  with  the  tern- 
perattire. 

lUuHtrations  of  capillary  action  are  abundant.  It  feeds  the 
lamp-llame  with  oil.  It  wets  the  whole  towel,  if  one  end  is  lef. 
for  a  time  in  a  bu«in  of  waiter.  Ft  draws  water  into  wood,  and 
causes  it  to  swell  with  a  force  sumcient  to  split  rocks,  and  to 
raise  large  weights.  I  low  does  a  little  water  in  a  wooden  tub 
prevent  its  falling  to  pieces? 

'  ^"1 ""y-  *«'>-""^<'-    '  ObBorvo  that  thro,.Rl,o.,t  tl.U  troatlHc  U,o  word  „8  exnrewe. 

«u  .x«ot  proponluu.    Wla.»  U,.r.  1«  n.t  an  exact  proj.o.llon,  the  word  Jk  ia  3 


I. 
II. 
III. 

IV. 


40 


MATTER   AND   ITS   PROPERTIES. 


noL!!;  °^°l«<'^lar  Phenomena. -Besides  the  phe- 

nomena we  nave  just  st.ulied,  there  are  a  great  many  others 
ependmg  .n  part  on  n.oleeular  attraetion,  but  much  a.o  e  on  the 
•no  ecuhu-  n.ot.ons,  of  which  we  learned  in  §  5,  page  6.     Many 

evenXrir"^^  ^"•"'  "^'  •'"'^^^'^"^^  ^"^  tl/explanation 
nete     r       •'"•     '^  ^'''"'  ^'  "-'^"3' complicated  and  ineom- 

Wnr       ^'T:^f  "'""''  ^^''"  ^'^^'^"  phenomena  are.o;«^/o„, 
oOsorption,  and  diffusion. 

su face  of  water.     Soon  water  is  drawn  up  into  the  pores  of  the 
nnp  by  cap.llary  action,  and  the  whole  lump,  including  the 

ll   umn  r    '""'^"''  ;r™^^  "'"•^^-     ^-^  you  discover  that 
the  1  mnp  becomes  smaller,  and  slowly  disappears  in  the  water. 
^Vhen  a  sohd  becomes  diffused  through  a  liquid,  it  is  said  to 

1.0  dissolved.     The  dissolving  liquid  is  called  a  solvent,  and  tl^ 
result,     ,        ,  J,  ^^j, .,  ^  ^^^^^^.^^^^     ^  ^_^  ^^.^,^  ^j.^^^^^^  ^ 

solid,  07ihj  When  the  adhesion  hetioeen  them  is  greater  than  the 
^^oAc^jon  zn  the  solid.  A  liquid  always  dissolves  a  solid  more 
i.'p.dly  at  first,  less  rapidly  as  the  adhesion  becomes  more  nearly 
satisfied  ;  and  when  it  is  completely  satisfied,  or  is  balanced  by 
the  cohesion  in  the  solid,  the  liquid  will  dissolve  no  more  of  the 
sohd  and  th  >  solution  is  said  to  be  saturated.  When  a  solution 
wul  take  nwch  more  of  a  solid,  it  is  said  to  be  dilute:  and 
concentrated,  when  it  will  take  little  or  no  more. 

If  the  solid  be  first  pulverized,  the  liquid  has  more  surface  on 
winch  to  act,  and  the  solid  is  dissolved  much  more  rapidlv 
irmt  generalh,  weakens  cohesion  more  than  it  tveakens  adhesion: 
hence,  with  few  exceptions,  hot  liquids  dissolve  solids  more 
rapidly  and  in  greater  quantities  than  cold  liquids.  Boilin^ 
water  dissolves  three  times  as  much  alum  as  cold  water;  conse! 
quently,  when  a  hot  .aturate<l  solution  of  alum  is  allowed  to 
eool  at  least  two-thirds  of  the  alum  must  be  restored  to  the 
«ol.d  state  (see  Ex'i,.  1,  §23),  while  one-third,  or  the  amount 


ABSORPTION  OF   GASES   BY  SOLffiS.  41 

that  the  cold  liquid  is  capable  of  dissolving,  remains  in  solution, 
llie  ie„,a„ung  solut.oii  ,s  called  the  mother.lup.or.      Lum   and 
u   few  other   substances,   are   dissolved    better   in  cold   w;"! 
t  rystals  of  such  substances  are  only  obtained  bj  gradual  evap- 
oration of  the  solvent.  ^  ^ 

Water  is  the  great  solvent.     When  we  speak  of  the  soh.bility  of  a 
substance,  water  is  always  lUKlcrstood  to  be  the  solvent  . 

other  liquid  is  speeiiied.     AVhy  is  it  fortunate      ,t   J^  ""' 

«o,ventP     Nan.  substances  that  waSl t^^  ^  :^  ^^^U^ 
many  substances  insoluble  in  water,  sou.e,  as  phosit^r^un^   ^d 
.esni,  flud  a  solveut  in  alcohol ;  sulphur,  in  bi-s,  iphile  of  c^rClea 
>»  mercury;    and  tats,  iu  ether  or  bcu^iue.      Would  von    .?,'  ' 

«  t^rniture  with  alcohol.    How  are  ^JIZJZ:::^^. 


\i 


m„luMhu  altmclmc,  and  is  ,i,.„„nll,i  »„j„,yi,,-„(.  c,.,.tai„  soli,!, 
pc.,s  »o  strong  ,u,  uttracti,,,,  fo,-  j,,..,  timt  thov  not  onl  •  d  Iw 
U.0  ga.cs  ,nto  tl,o  s.nall  oavitic,  or  l.olcs  within  then,,  l,nt  groZ 
condense  ti,e,„  tlK.,-o.  It  should  be  earefnlly  „„,^,,  |f4  'ho 
attraction  i„  this  case  is  generally  between  L  .  Js  tri  the 
»,/««,  or  ».«,■„»,  and  is  hence  called  ..,«;:,  in  dU 
tmetron  fron,  „U,>n,M,c,aar  a,t.«,ion,  which  is  tife  „a„e  given 
to  the  phenomenon  when  gases  arc  taken  tato  the  porJotl 

r.-oshly.bumed  charcoal  placed  in  dry  air,  may,  i„  a  few  dave 
have  ,t,  wcght  increased  one-tiftieth  in  conse,, ,  nee  „f  The  a^ 
that  ,t  absorbs.  (Has  air  weight?)  The  attra  tion  of d  arcoj 
for  „„x-,ous  gases  is  especially  great,  n.aking  it  very  e fflcto^ 
.0  cleaning  the  air  i„  hospitals,  au,l  in  .^noving  ,,o^i„  ! 
odors  Irom  p„tr,d  animal  and  vegetable  matter  by  abs^l  Z  the 
foul  gases  that  are  generated.  It  docs  not  check  d  ca^'  but 
rather  hastens  it.     K  r.,t,  which  had  been  baried  in  cha  eol 

teft  but    he  ha,r  and  bones,  yet  no  bad  odor  was  perceptible. 
v»  liy  do  farmers  mix  muck  with  manures  ? 


42 


I      l.;i 


i 


MATTBIt  ANf,  m   VHOl^mTtEH. 


§38.    Absorption  of  irai,e»  by  linuidM      ,/.       , 
teinp<.rut.iro  of  0°  CV„     Ja  ,<«,.„, ,         '^"'"^""Mf'     Water,  at  a 

cim.,.,.i  with  ti.iH  ,.1 :::,'' :;  ""^-"^*  ^-^  wat.-  thus 

of  gUH  that  a  n,uid  Hi ,  IC  IH      """"  r*"''-''    '^^''«  """-'"' 
water"    i«  «iu  pir^aflr    '^^  "  «o^J- 

'.".-or..e.t,ji.;:t;s::t,::^ 

u»e   l«   removed  a  Iur«t'   „art  „f  ^^»'«"  .the  prcss- 

efferveseence.  "^^    ^^'^   m-apt-M,    cnushig 

i^  39.    Free  diffii«ion  ^  liauid«      ,/ 

Hii«  cttwc-'/  '  ni\%\u^  or  (liffiLsioii  in 

I  ''X|><^rim<fn(  »,    Take  rIm ,^    *  , . 

"'•  i''<n  u,  «Tm  Jl   ,  I*"  f  '^  """•«"  Particle 

HnU  any  l,„ll,.ai ion«  „t  mn.\m^  "''•'  ^'"'  **  week.    Do  yo« 


ttihc  nearly  /ill 


It  In  poHHlhl,.,  and  even  /•r<*l«iM«'  flmt  i,.  ,i,i 
there  Is  u  ./..«,>«/  ,.„,!„  \^^ZuZl    "'";":"""'"''''  "^  "'-^ter,  but 

of  heat  d«.eo„,pom..  ihe  hy<lr«i  trn^i.  T^  '^"*  '"*'  ''''"' "f'l'Ii'atiou 
which  lutt..r  then  .Heup.^  '  S;/Tr  *"  T''  """  «"'"""'"'  «'»«> 
dioxide  (.„„„»».  -alld.a^lj^, '"  :7'*"";' ->'«^'-"  -r  ca;bo,; 
.•.xt..nt  there  Ih  a  ehe.nleal  unlonXeln  H  ^      *""'"'  '""""'''^  "'  -""« 


blFPUSION  OF   LIQUIDS. 


4A 


Fig.  17 


If,  (lm-;.;jr  the  operation  of  diffusion  in 

he  last  tlu-oc  experiments,  yon  exanane 
he  l.quKlw,th  a  microscope,  yon  ^ill  not 
be  able  to  trace  any  cnrrents  ;  hence  the 
raot.o„  of  liquids  in  diffusion  is  not  in 
mass,  but  in  molecules,  -  a  kind  of  inter- 
mole,  ular  motion.     We  learn  (hat  s„me 
J'Q'nds,  even  when  stirred  together,  will 
"ot  remain  mixed;  while  others,  who.e 
densities  are  very  different,  when  tnerely 
placed  m  contact  with  edch  other,  slowly 
mix  of  themselves.  ^ 

porous    partitions.  -Osmose 

bottle  ?   r         k""°'"    "'    ''    ^'>"i<^->l"«>'H„c.,I 

.lass  t«.e  pas^i  u^^h  u(;"- :^;;^  "t^^^:,  -  ^-^^  '^-'-^  ^ 

a    piece  of  gold-bouter's-skia   or  ^J,l\'  "     '^  •'^■''''  ^''"  ''"«"'" 

With  a  concentrated  sohu';;;  :;  .^^r  ""'   ^""    """"• 

corknUothebottlesothattlu,liq„Ki  '  K,,n  rl'T"'  """  "'•'^•^^  ""• 
•say  at  a.     Now  snspen.l  the  an  a  '  "'  "■"^'  ""  ^"«  t"'^^'' 

the  >tton,  n.ay  be  covere.l.  I  ave  f,-  '"  ?'^"'  "'  ''■'''"''  -'  »"«' 
carefully  examine.  What  Is  fho  .'<!.,;  i ' ',  "T  '"'  """"'  ''""'  ^'"■" 
Pl-OVC?  '*'^''"^      ^^ '"'t  (Iocs  this,. xp,.,.i,„ei.L 

When    liquids    or   ^ases   fnr.u.    <i    • 
«epta,^    and    mix  wi^    .       ;,,  '''''V^'V'''"'^''    "^*'•^- 
osmose:^     To   distinon Ll  '      '"   •''*^'""""    '^    '••■'"^"<S 

Of   the  liquid  ^gns«::Tf"  '*''''^ 

^  s  towauls  that  which  nicreases  in  volume 

See  Appendix,  Section  B  2  ^,.„, 


N  i'ff 


:.i 


h 


t. 


HI 

I 

m 


44 


MATTEU   AND   ITS    iMtOI-KIlTIEH. 


Fig.  18. 


l::f '  -^^.....,.  .uul  the  opposite  oun.nt  is  cal.e.  .... 
are  called  o;;r/orfre:r%  ^'"-^^"""'^  -'^^'^ 

The  principle  ,f  un;,.::^;;^:;^:^  Lll^'^^'T^-^ 

finds  important  a,)plieation  in  chenncV  "^     '"''^'^ 

and  pharmaceutical  laboratories.  For 
example,  from  a  rod  (Fig.  ]8)  is  sus- 
pended a  glass  vessel  having  a  bottom 
of  parchment  paper.     «„,(,  .,  ,,,,,,.,  j^ 

called  a  .Z.«/y.,,.  j^  y^^  ^ 
P  aced,  for  instance,  the  liquid  contend 
ot  the  stomach  or  intestines  of  a  detid 
annual,  suspected  of  containing  some 
IXiison,  and  the  vessel  is  floated  in  a 
vessel  of  water.     If  either  arsenic  or 

SZnir" ''  ^''''''"*  '^^•■"  ^^P-'^^'-'^te  from 

the  albummous  matter  in  the  food,  and 

pass  through  the  septum  into  the  water      Th. 

-atmg  ,„i.ed  liquids  b,  osn.ose  iltu;.,  ^^^"^  ^^  ^^P" 

a"fl  tl.rust  i„  a  li-^hted  siXor  '«st-tul,o  with  oxj-cn  ^as, 

than  i„  the  air.     l'     a         c  r  tnhl"  ^';  '"^'V'"™'^  '"'""  '"-^'  ™P^W 
tube  hivortcHl  Mor  t  is    1        •       l'''^''  '"ydroj^en  gas,  and  keo,    the 
there  will  ho  1;  ^.!  ^^:;'S.f «";; «'^-'  *!--  M.htcr  thai.  ^  " 
the  gas  takes  Are,  am    ,^  n   ,^^t  '  ;r  n     ^''''''' '"  '^  "^'"^^"*'  «''""^^''- 
Next  ,11,  one  tube  wit       "J.;    'an    t    T  ''  ""  '""'*"  "^  "'«  ^'"^- 
Place  the  ,„outh  of  the  .at    ;      ;Tho     0^;^^^^^^^      ^'"^^^'^"'  ''^'  ^'^^ 


:  En<inRmose,  h„aard  impulse. 
fixosmoae,  outimrd  impulse. 


'  Crystiilloid,  like  crystal. 
*  CoUoM,  like  ffum. 


DIFFUSION  OF   GASES. 


45 


ii 


o.v,„„  ana  ,,,v.,,.„«.n,r;;;',;:;::;;:: :':,;;;;; "'"-  ■'-"  -'  '^- 


Many  pairs  of  liquids  do  ii,>t  ilimi 


FifT.  m. 


/,„«,7,rt-        .,         '        ■"  "'■'*'^ '"to  <;ac]i  otlicr,  hut  fcprw 

.7-  .^ir«...  ..o  e..-,  o,.r,a.^  .„,  ^  is  i.npo.sihle  t<Mn-evo.rt^ 

gases  Ironi  mixing  wl.on  phicc-d  in  contact. 
(It  IS  tlionght  best  to  introdnco  the  snlyect  of 
<''<i"s.on  of  li.inids  an,l  gases  in  ti.is  place, 
<l'<"'yli  It  lias  little  or  no  connection  with  tlie 
«"l.)eet  of  adl.esion.  'J'he  explanation  of 
(I'M.is.on  n.nst  he  deferrcl  to  its  proper  place 
in  the  chapter  on  Heat,  §  128. 

In  c„nsoqnon,.c  of  this  universal  tonclency  to 
'"  l-Mo,,,  ^...s,-s  will  „„t  remain  se,)arated, -e> 

u  S  "  n  f  "'^  "T'!  '  '"^"^^'  "^  '^'^  '--^^  "i-n 

".lU..     Jlus   ,s  of   nnn.ensc  importance  in  the 
-•.>non.y  of  nature.     The  largest  portion  of  our 
atmosphere  consists  of  a  mixture  of  oxygen  and 
"Urogen  gases.     There  are  ahvays  present  lo 
-.all  .iuantitles  of  other  gases,  such  as  carbomc- 
acul  gas,  anunonia  gas,  and  various  other  gases 
^vluch  are  generated   by  the   decon.position   of 
orgame  n.atter.    These  gases,  obe.Uent  to  gravity 
alone,  would   arrange   themselves   aeconhng  to 

then- weight, -earbonie-acid  gas  at  the  botC 
.-.  nitrogen,  annnonS,      d  o   ^r^!^:  ^  "Sr'  ''"^T"''  ''  ^'^^- 

P.oporUo^..l^th;^r;— '^^^^^^^^^^ 

S  42.  Diffusion  of  gaaea  through  porous  n«rt-iH™. 

motion;  very  complex,  m^eQufcw 


Ml 

1      II 


46 


MATTER   AND   ITS   PROPERTIES. 


Experiment.    Take  a  thin 


Riinsen's  battery  (§  ifiS),  a.id   pi 


unglazed  earthen  enp,  such  as  is  used  in 


end  witli  a  cork  tl 


g  up  the  open 


^  V,        ,  irough  wJiJch  extends  a  "-l-iss 

tube.     Place  the  exposed  end  of  the  tube  in  a^ cup 

^dro^-en  or  coal-gas,  over  the  porous  cup,  as  in 

■gure  20.     Observe  carefully  what   takes  pLe 

Ion  do  you  explain  the  result?    Ren.ove  the  glass 

e  d  to   .'       ''"''"'    ''"^^  *"«  '-^^-^'t  •"  "-case 
lead  to  the  same  conclusion  as  that  in  the  lirst^ 

of  a  t.ghtly-stopped  vessel,  and   having  another 

«hiss  tube  pass  through 
an(,tlier  perforation  in 
'he  same  coik,  water  is 
i'>iced  out  in  a  jet  sev- 
eral feet  in  hight,  when 
tlie  liydrogen  jar  is  held 
over  tlie  porous  cup. 

Cliildreu  well  understand  that  toy-balloons 
^vluch  are  made  of  collodion  and  filled  with 
e^ml-gas,  collapse  in  a  few  hours  after  they  are 
"•fiatcd.  What  is  the  cause?  Nature  furnishes 
an  dlustration  of  osmose  of  gases  in  respira- 
tion. In  the  lungs  the  blood  is  separated  from 

vpi„«      P    1      •        .  **"■  '^^  "'*^  *'^'"'  "lembranous  walls  of  the 

veins.     Carbon.c-acid  gas  escapes  from  the  blood  throu-.h  these  sentr 
and  oxygen  gas  enters  the  blood  through  the  same  sepia  '    ' 


ised  ia 


CHAPTER    n. 

DYNAMICS. 


)ons, 
with 
fare 
shes 
ai  ra- 
re m 
file 
pta, 


IV.     DYNAMICS   OF  FLUms. 
§  43.  Equilibrium,  pressure,  and  tension.  _  That  branch 
of  scjeneo  vvh.ch  treats  of  forcv  an.l  the  ^notions  it  pro  h  0'"  s 
caned  dynamics.     It  has  boon  shown  that  force  may  a    "n 
bodytop..duce  „.otionorrest;  also  that  two  or  Joi'fo    0* 
may  so  act  on  a  body  as  to  neutralize  each  other's  effect   T 
the  la  ter  case,  the  body  continues  in  the  same  condit  on   either 
Of  mot.on  or  rest   as  if  it  were  independent  of  the  action  o       e 
forces,  and  .s  saul  to  be  in  e,uiU,nuW  and  the  forces  Tctbl 
on  It  are  also  said  to  bo  in  cqnilibrinm.     Inasmuch  as  no  boy 
IS    ver  free  from  the  action  of  force,  it  must  be  that  a  loTyZ 
rest  IS  in  a  state  of  equilUmum.  ^ 

If  any  portion  of  a  force  is  r.ot  effective  in  producing  motion 
-  t.e.,  If  par  or  all  of  it  is  exerted  against  other  forces  - 1  ^^  e 
may  result  w  at  is  called  a  ,.....•.  on  the  body;  T^hen  wo 
push  on  a  wall  or  on  a  heavy  sled  n.oving  over  the  ic  or  ! 
book  presses  the  table.  The  same  force  which  cans  a  i;"  to 
fall  when  unsupported,  causes  it  to  press  on  any  obsU^cl  "^i,,^ 
♦preven  s  ,t  fron,  falling.  Or,  if  the  force  is  e4rted  o  VZlv 
m  whK.h  the  n.olecular  attraction  is  strong,  -_  "  0  T^^' 
we  may  have  a  pull  or  tension,  as  when  Z.  Inn..  ^  .u 
^a^s„ma.bberband.     If  t,.; bod^:;: Z^-^ 

convenient.  ThecaseofunifLvi:^;;^;:^:::-^^ 

» Equllibriuin,  equal  balance. 


48 


I>VNAMICU 


liv  f !;♦?>..  •  ''^i^'"^'^'''y  a»tl  those  occasbnofl 

»)3   difference  m  compressibility  an-l  exDausibilitv    li. 

gasesaregcvernedbv  the  same  laws    Ts.  u^^^  T       '"^^ 

then  together,  in  so  far  as  they  uralike  ^  n  Ir  h  ""'  '""'^* 

of  jitud.  '  ^"^  common  term 

Of"™;:  'Tllr'""  """  "•"  "-  i"-«'  ™-  «-  '.orders 

air  reqnn-es  spec  a     e\'i)erimoiif«        ir         i  ["^s^uit  or 

w.litni.s.ilh..ter;lj:e^ 

lH•a^  ,er  thereby  ;  the  downward  pressu.e  is  not  felt,     liut  wlut 
v..  ra.se  a  pailful  ont  of  the  water,  it  suddenly  become    LJ^^ 

If  we  could  raise  a  pailful  of  air  out  ^' 

of  the  ocean  of  air,  might  not  the 

weight  of  the  air  become  perceptible  ? 

If  we  dive  to  the  bottom  of  a  pond 
of  water,  we  do  not  feel  the  weight 
of  the  i)ond  resting  upon  P'^.  We'do 
not  feel  the  weight  of  the  atmospheric 
ocean  resting  upon  us  ;  but  we  should 
remember  that  our  situation  with  ref- 
orence  to  the  air  is  like  that  of  a 
diver  with  reference  to  water. 

Experiment  1.  Fill  two  glass  jars  rPlcr  99^  „  •.,,       . 
glass  bottom,  B  a  i.otto.n  provi,lc7hv  ^     ^^  '''''*"*'  ^  ^''^'"^  * 

tightly  over  the  rim.     inve  t  b  n  T"!'  "  "'""'  "'  •^heot-rnhhor 

iiiNtii  uotli  i„  u  lap^rer  vessel  of  water,  C. 


Fig.  22. 


PnESStTRE  m  PLTTIDS. 


49 

What  forre  sustains  the  water  in  A  ?     WT.nf  „      i     .^ 

;;.;ta...  ..h  ......u.  W  .  L^hC  h;tr:r  b^^ 

j:::s^tr«;S^;-x^^^^^^^^ 

feel?  Why?  Remove  the  finger,  and  he  ZZ  the  t  h  f '"" 
sinks  to  the  level  of  the  waterin  vessel  C      ^v?"'      "  •     r^"' 

we  find  that  the  downward  pressureof  air  ^es  ri  ^an  "nf '''": 
pressure  in  the  liqnid.  In  this  respect  fluids  S!Z  wil-U  i  ^  ^ 
whose  molecules  are  so  rtrndy  hehl  to-ether  tl.af  u  .„  '""  ^"''''•'• 
pushed  in  any  direction,  that  pirtdra^stlTerJstwit'h^i^^^^^  '^"^  ''''  '' 
^n7n  vT'"''  ^''^""*''^  f^'-  «'at«^  '>ci"ff  sustained  in  the  vessels  A  B 

the  a?;  T  VI  '^''"''""^'  '^'•^'•"'^^  '^^  "-  downward  pTetu'e  of 
the  air.    Does  this  downward  pressure  cr-afe  in  ,.,»,..,..  i  ^      ^^^  ^^ 

...0  ..r  use,,,  »„  .ha.    ,r  .„„  vLe,,  L^nrLr^Tl^Sr^ho' 
Finr.  23  water  will  not  fall  out? 

Experiment  2.  Keeping  the  finger  pressed  on  the 

vlr      T^'"'  ;*  "'r''  ""'  ^'"-"^^"^  «"'  «f  the 
water.     The  water  does  not  fall  out.     Why?    Slio 

a  tlun  glass  plate,  or  a  piece  of  thick  pasteboard, 

under  the  mouth  of  A,  and.  pressing  it  against  the 

mouth,  raise  the  vessel  carefully  out  of  the  water 

and  remove  the  hand  from  the  plate.     The  water 

does  not  fall  out,  nor  does  the  plate  fall.    Why? 

Experiment  3.  Force  a  tin  pail  (Fig.  23),  having 

Does  ilowuwaid  pressure  cause  a  lateral  pressure? 

Eiperlment  4.  Make  holes,  at  dlUferent  depths  In  the  sM„  „f  . 
«el  ,F,g.  24)  co„u,„„«  water.    Water  Issue,  '»"„„:,"  ,:'o™' 
erable  force,  from  tjie  orifices.     Why?  consid- 

ExperimentS.    Bind  a  piece  of  thin  sheet-rubber  tightly  over  a 


60 


BVKAMIOs. 


*'ig.  24. 


Is  the  result  no  matter  in 
what  position  the  bottle  is 
placed?  What  lesson  does 
this  teach? 

Experiment  6.  The 
Majrdelnirg  hemispheres 
(Fig.  25)  are  two  hemis- 
pherical cups,  having 
their  edges  made  smooth 
so  as  to  be  "air-tiglit" 
when  placed  in  contact. 

tl'o^Z'^sLT:',"'"''^  '""''^-  ^"^  "^  ^"« '--"-  -»--ts  of 

The  stJinM       K         "  '■'"^'' "•"  '"'"  •'^'•^'^  '*^''""  ^-onnected  by  a  screw 
I  he  stem  has  a  bore  passing  througl,  it,  and  a  stop-cock 

screw  t?!f'    .  "r  '"'^^  *"  '""''^^''  ^^'»°^«  the  ring, 
tl.e  ail  f  om  the  sphere;  then  close  the  stop-cock  and 

J'o  ding  tlie  sphere  in  any  position  they  choose,  can  onlv 

with  great  dilHculty  pull  them  apart.     Why?'  ^ 

Boys  amuse  themselves  by  lifting  l,ricks  (Fig.  2f5)  with 

Fig.  26.       a  circular  piece  of  leather,  ii.oisteued  and 

pressed  against  the  surface  of  f.ic  brick,  so  as 

to  exclude  the  air.   The  pressure  of  air  against 

tlie  leather  l)iuds  it  to  the  brick  in  whatever 

position  placed. 

We  (oiulude  that  gravity  causes  pressure  in  a  body 
ofjtidd  in  all  directions. 

§  45.  Pressure  increases  with  the  depth.  -  In  the  ex 
IKMument  with  the  vensel  with  apertures  in  L  side  (iT^ 
we  find  that  the  deeper  >.e  orlflee,  the  greater  the  velooify  of 
t^.e  stream.  And  in  the  experiu.ent  with  the  wi,Ie-,„ou.  .e, 
br^  le  covered  w.th  rubber,  we  (h.d  that,  at  the  same  depth,  the 
1^..  I  pr.,-.,<o  i.,„,a.d  ecjually  in  aii  directions,  but,  as  it  ia 
carried  to  greater  depths,  the  piossure  is  increased. 


I 


PRESSURE  EQUAL. 


51 


I 


Fig.  28. 


Fif 27    1?  ^'"  '"'''  ''""*  '"  *'"^  ^°'''"  represented  by  a, 

Fig.  27,  place  mercury  ,n  the  lower  part  of  the  tube,  so  as  to  fill  the 
short  arm,  and  ir,-adually  lovver  the  tube  into  a 
deep  vessel  of  water.     Sink  tlie  tube  to  diflerent 
depths,  and  carefully  watch  the  column  of  mer- 
ci»ry.  What  Is  the  result?     What  does  it  teach? 

M  46.  Pressure  at  any  point  in  a  fluid 
jgual  in  all  directions.  -  Experiment  i. 
Introduce  anc.iher  tube,  containinjj  mercury,  of 
the  form  represented  by  6,  Fig.  27;  lower  both 
tubes  so  that  the  orillces  in  the  water  shall  be  at 
the  same  level.  Observe  the  column  of  mercury 
lu  each  tube.    What  does  the  experin)ent  prove? 

:- Experiment  2.  Gem- one  end  of  a  lamp-chimney  (Fi...  28)  with  a 
orcnlar  piece  of  leather,  and  suspend"  fron.  the  hand  by 
."'.•u.sofa  string  attached  to  the  center  of  the  leather 
and  passmg  through  the  chimney.  Hold  the  leather 
flrndy  aga.nst  the  botton,  of  the  chimney,  and  lower  tl^ 
covered  end  a  little  way  into  a  vessel  of  wat^  1^^ 
m.y  now  drop  the  string,  and  the  upward  pressure  of 
the  water  will  keep  the  leather  in  place.  Pour  witer 
-slow  y.nto  the  chinn.ey  until  the  leather  falls.  Wha 
i«ht  does  the  water  reach  in  the  lan.p-chimney  befor 

1  nJiif  r'V     :'    •''"^'  '"""'^  '^  ^"^■"  '■'^"'^   ^^'>y  ''-«  "o 
a  i)iUlful  of  water  in  a  well  sociii  licavj? 

■   '*''!''  T"!'!  "f  «''l'«"">"nl«  thus  far  show  that,  at  even  ,»,■„( 
.,.«(,.,;,  o/JI.„;i,  ;„nvU,j  «.„«  pressure  ,o  l,e  «,,.,(  J„ ,? 
.  «  *r«,o,„,  anatlua  ,n  ll„a„s  tte  pressure  increasj.  ZZ 
<hph  rncrea.e..     It  »ho„l,l  also  l,o  observed  that,  th,  .UreJZ 

uglU  avglen  to  the  surface. 


i>.  ■ ; 

i'  ': 


'1l 

-i) 

,'iif 

I 


52 


DYN  Allies. 


Flir.  29. 


cnry  In  the  closorl  arm  will  sink  abont  20-  to  A,  and  will  rise  2cm  („  the 
open  arn,  to  C;  l,nt  the  surface  A  is  TO-  higher  than  the  surface  C. 
i  ins  can  l)e  accounted  for  only  by  the  atmos- 
pli^.'c  i)ressurc.  The  colunni  of  mercury  BA 
containing  TO'-",  is  an  exact  counterpoise  for  a 
t-ohnnn  of  air  of  the  same  ,liameter  extending 
from  C  to  the  upper  limit  of  the  atmospheric 
ocean, —un  unknown  liight. 

Tho  weight  of  tho  7G™"'  of  mercury  in  the 
column  IJA  is  l();?,'5.3s  exactly,  but,  for 
convenience,  nmy  be  said  to  be  about  1^. 
Hence  the  wei-ht  of  u  colunni  of  air  of 
1'""'  section,  ('xtentling  from  the  surface  of 
the  sea  to  the  ui)i)er  lin)itof  the  atmosphere, 
F'g-  30.  isat)outl''.    Rnt 

gravity  causes 
equal  pressure 
in  all  directions. 
Hence,  at  the 
tcrd  (if  the  .sea, 

all  hijtUes   arc  pressed  vpon  in  all 
diredm,s  by  the  afmosjyhere,  with  a 
force  of  about  P  per  srpmre  centi^ 
meter,  about  15 pounds  {exactly  14.7 
lbs.)  per  square  inch,  or  about  one 
ton  per  square  foot.     Fluid  pressm-e 
is    <X("iierally    expressed    in    atnios^ 
l)heres.     An  atmosphere  (when   the 
term  is  used  to  denote  i)ressin-e)  is 
the  pressure  of  P  per  square  centi- 
meter. 

.  ..,.„,  ,    ,  '^  ""^"  "f  average  size  sustains  an  ex- 

ternal pressure  of  about  lifteen  tons.  If  the  area  of  the  bntto.n  of  .an 
••  empiy  pad  is  one  sc,uare  foot,  the  downward  pressure  on  Its  bottom 
is  a  little  more  than  one  ton;  how  can  any  person  carrv  such  a  paU? 
ftoa  whj'  l8  Its  bottom  ijo(  forceU  vut? 


BAEOMETER. 


53 


Fig.  31. 


§  47.  Barometer.  —  Figure  30  represents  another  form  of  ap- 
paratus, which  is  moreeommouly  used  for  ascertaining  atmosplienc 
pressure.  It  consists  of  a  straight  tube  about  8o""  long,  closed  at 
one  end,  and  filled  witli  mercury.    When  this  tube  is  inverted,  tlie 

open    end   having 

been  covered  with  a 
finger  and  plunged 
into  an  open  cup  of 
mercury,  and   the 
linger    withdrawn, 
the  mercur_y  in  the 
tul)e  will  sink  till 
it  balances  the  at- 
mospheric    press- 
ure.    This  experi- 
ment was  devised 
by    Torricelli,    an 
Italian.     The   ap- 
paratus is  called  a 
barometer.  ^      The 
empty  space  above 
the  mercury  in  the 
tubeis  called  a  Tbr- 
dceUian    vacuum. 
The  history  of  this 
experiment  is  very 
interesting  and  im- 
l)ortant,  inasmuch 
as  it  was  the  rirst 
demonstration     of 
the  pressure  of  the 
atmoaphore,     CSee 
Whewell's  History  of  Inductive  Sciences,  Vol.  I.,  page  345.) 
The  hight  of  the  barometric  colinnu  is  subject  to  fluctuutions  ; 
*  Barometer,  weight  meatunr, 


54 


DYNAMICS. 


this  shows  that  the  atmospheric  pressurp  ,'«  «„w    .  * 

frpm  vaMous  causes.     The  baron^^T  IXa.^^^ 

tor  of  all  changes  -'n  atmospheric  presst^^  'it  if      """"" 

able  as  a  weather  indicator      Not  fiT  '*"  '''^^"'- 

which    mercury   may   stand    Zl  f"'  ^"^' ^'^^'^^^^^^^  point  at 

mercury  constantly  falls  as  the  ascent  increas  s      T^.f '     '' 
that  the  pressure  is  greater  near  the  bottom  of  fh'o  ,  ' 

than  near  its  top.     It  is  found  tZ,  T  """^"^^  ^'^^" 

rapidly  near  tl  o  hnfV         '  ^"^  ^'""''"'^  ^"^^'^^ses  very 

Fig  re  31      T       ,^"  *"'"'  '^^^  ^"^-^3'  be  understood  by  studying 
air      Th Vr  '^'"^'  '^^^'  '^'  ^'-^"^"^^  i"  density  of   hf 

Xre^;;^—::::^^^^^  r  "^  '^^^^^^  ^  ^^'^^ 

the  mercury,  i^  inches      tL  f  ^orresponding  hight  of 

cobjnma,«;,,^-:,^-age^ 

It  will  bo  see,,  that  the  deusitv  at  a  hi.rl,t  „f  a      ,      ■    ■ 
mtio  „„.o  tha„  ,  the  density  at  tJ-ole:.,'  f     "a't     ;:: S  7  .'•^ 

""'y  Ttmni'  so  that  the  greatest  part  of  the  at,inn«„i,....<.        [  , 
within  that  distauoo  of  the  surfa  e  of    he  elrtr  ar,:™', 
hand  if  ™  opening  conld  be  n.ade  i  nthe  ea.'th  3V   ile 
depth  below  the  sea-levcl,  it  is  cale„lato.I  tmt  th'  d.!,'  itvt^^,,;" 
mr  at  the  bottom  wonld  be  1,000  tin,es  greater  a,   a  Ve     n 
level,  so  that  water  would  float  in  it      Ai,.  l,„    i,  " 

to  this  density.  '^"  *""  '''<'''  """P-essed 

To  what  hight  the  atmosphere  extends  is  unknown      u  ■ 
variously  estimated  at  (h>m  50  to  200  .nill      IfHl         ,        " 
were  of  unifo™  density,  and  of  the  ^mt  de    ,    "  [' i    ir: 
the  sea-level,  its  depth  wonld  be  a  little  short  oflve  Ze 
Certa,,,  peaks  of  the  Hin.alayas  would  rise  abo  "  it    "iT  t 

'  bjt  the  aid  of  a  barometer.  ^ 


> 


reauii 

ma 


COMPRESSIBILITY  AXD   fiXPANSIBILITY. 
QUESTIONS. 


the  Dottom  ?  ^         "  '^'"^'°  «"»■".  "»'  Hf  would  at 

life  ?  °^  ""  '»  '•  B"™  tunc,  in  c.-dcr  to  sustato 

pa'o?trz.,:rrof„,fr:  n,r°°" '»-'  -"-  ■'-'>''«>°-> 
ati:,r;;:':;:;*;;;;r /"'■'-  -"^» -»^™;  >v„„t  ,s  ..e 

§4a  Compressibility  and  ejtpansibility  of  saa«,      t., 
."c-aase  of  p,v..,„-c  attending  the  inc-oase  L  floitr  i,rh!t,' 
.qinds  aud  gases,  is  readily  explained  byti.e  faet  tl      th    lo 
layers  of  fluids  sustain  tl,e  weight  of  all   |,e  la™,     te      7°" 
seaueutly,  if  the  body  of  fluid  is  of  uniform  d.,!,'  • 

nearly  the  case  in  liquids,  the  pressnr    wi  ^   '  Z'Z7 

the  same  ratio  as  the  depth  increases     lint  Z  ''*' 

fa,,  f,™  bohtg  of  nnifo,™  doi.sity,  i ,  L  "!  ,    !  7;f  °7"  " 
compressibility  of  gaseous  mutte^     The  e      rast  Zt  "" 

and  air,  in  this  respeet,  m.ay  be  seen  i,  theZt  i  f       '  "'" 
Jeeted  to  a  pressure,  of  onl  atinos,;::: '  Jr,   f  S;'™"; 

The  pressure  at  difforonf  rIor>tJic  :.,  v     -i 
by  piling  several  biiX To  ot  anotl     '  !!1      T'       '"'""■'"'" 
difforem  bricks  snstai,,    I^  d^c  ;  ;Tth  "th  "  TT".'  '""' 
the  upper  surface  of  the  pile.    On    ,e  ot '         '  1   '         '""' 
gases  at  different  d,.,.,h,  T-,'^,"Jr  f  '  "'''"""™  "' 

wool  one  on  anothe;:  ^  SI,  ce  h  vl l,™:  !?  "'"7  ""'""'" 
«eeoc  varies  with  the  weight  it  bl!  t";rel::l|  .'rr 
eat  fleeces  snston,  are  not  proportional  to  their  respective  dept; 


:: 


pi  I 


t)6 


PVN'AMHH. 


below  the  upper  mirfiieo.  of  fj,,.  njlp       At  t^t      ,u      ^      , 

to.-ce  exerted  i,.  .v,!,.,.,  ,  tl  1     Jrr''  '"T'^ 
will  «!«,.  c„m„I...,v  'r.^Z  ZtrSlTT"''"''  " 

i«  removed,  i,i,,„i„,  .J  ,»,.,,„1""  ,^"j^  r^J;" "-;  p'-^-' 

St  ted  fli.if  maur,.  '  <  ia»ticity.    It  }m»  jilready  been 

Seated  that  matter  in  a  ga«eoi,i,  »tate    expand*  fndefinifelv 
ui)le,ssri.Htmine(Jbvcxf<.nj'tlforr.«      'ij       **      ,     imietimtely, 
to  the  .  nth  hv  f  1.  f  ;  -  ^^'"'^I'^'ere  is  confined 

tu  LUC  >  uMi  oy  t)](!  fojw!  of  gmvjtv. 

oompletoly  InfJuti,,^  tJi,>  |,ttiu,„v  ,,,^.,.  j^ 
...uler  the  gluHH  rocdv...  of  «„  «),.,„„, 
(lM<.r.  31)    tt.ui  .xhau^t  tl.«   «Jr,     What  i. 

tlie  receiver,  the  balloon 
HiiHtaiijK  a  prewurc  of  ir, 
f'oiindH  OM  every  w/uare 
i'H'li.  Wlmt  prevent*  a  col- 
li I>HemKi,.r  thfx  prexfiire? 
I'mwrnuch  m   the   balloon 

hIi'»VV«   no   «ltff,«  o/  dlMt*;n- 

'i'"'.     or    colhip^e.    until ^^ 

plficed  nnder  the  ree«»Jvpi-  u  ^.   ,. 

tension  of  tiLrtvH:.  *"  "*'^'"^  ''«'«"'^«^«  ^>y  ti. 

for  the  purpose  of  m^al!^Z'i^£::n  "l'"  ^'"^j/'''^'^^  (Fig.  33) 
orUlnar,  Ue.lt,.  the,  are  -ci  Jf^r^:;:,  ,j;^--«  -  o. 


f1|t.  32, 


Fig,  33, 


THE  AIE-PUTMP. 


5T 


,4 


1^' 


ments  of  ^^lass  in  all  directions  ""'"''  *'™^'"«  ^^'^S- 

to  ulax  rtse  1,  wlien  opporttnuty  is  given.  Since  this  elastic 
^rco  at  the  bottcn  of  the  cohnnn  exactly  balances  the  fo  e  of 
g  av.ty  act.ng  on  the  whole  column,  i.e.,  equals  the  weight  of  the 
whole  column,  it  follows  that,  at  the  sea-level,  the  elastic  fhZ 
of  mr  IS  ordinarily  P  per  square  centimeter.  ^ 

§  49.   Air-pump.  -  The  air-pump,  as  its  name   imnlies    is 
used  to  w.th<h.aw  air  fron,  a  dosed  vessel.     Figure  34  wk  serve 

to  illustrate  its  oper- 
ation.    R  is  a  glass 
receiver  from  which 
air  is  to  be  exhausted. 
B  is  a  hollow  cylin- 
der of  brass,  called 
the  pump-barrel.     A 
plug  P,  called  a  pis- 
ton, is  fitted  to  the 
interior  of  the  barrel, 
and  can    be   moved 
up  and  down  by  the 
handle  H;    s  and  t 
are  valves.     A  valve 
^  acts  on  the  principle 

of  a  door  mtended  to  open  or  close  a  passage.  If  you  walk 
.igamst  a  door  on  one  side,  it  opens  and  allows  301.  to  pass  ;  but 
If  you  walk  against  it  on  the  other  side,  it  closes  the  passaoe, 
and  stops  your  progress.  Suppose  the  piston  to  be  iu  the  let 
of  descendmg.  The  compression  of  the  air  in  B  closes  the  valve 
,  and  opens  the  valve  .,  and  the  enclosed  air  escapes.  After 
the  piston  reaches  the  bottom  of  the  barrel,  it  begins  its  ascent ; 
when  the  air  above  the  piston,  in  attempting  to  rush  down 


f. 


m 


58 


DYKAMICS. 


■/■I 

! 


to  fil    the  vacuum   that  is  formed  between  the  bottom  of  the 
barrel  and   the  piston,  closes  the  valve  ..     But  as  soon  as  a 
vacuum  is  formed  above  t,  and  the  downward  pressure  on  the 
valve  removed,  the  air  in  R  expands,  opens  the  valve  t,  and  fills 
the  space  u.  B  that  would  otherwise  be  a  vacuum.     Btlt,  as  the 
au-  m  R  expands,  it  becomes  rarefied  ;  and,  as  there  is  less  air, 
o  there  .s  less  tension.     The  external  pressure  of  the  air  on  R 
emg  no  longer  balanced  by  the  tension  of  the  air  within,  pressed 
the     ece.ver  firmly  upon  the  plate   L.     Each   repetition  of  a 
doube  stroke  of  the  piston  removes  a  portion  of  the'air  reml! 
ing  m  R.     The  air  is  removed  from  R  by  its  own  expansion 
owever  far  the  process  of  exhaustion   may  be   carded      he 
lec  iver  will  always  be  filled  with  air,  although  it  may  be  exceed! 
.ngly  rarefied      The  operation  of  exhaustion  is  practically  ended 

valve  t  "' '''"  "'  '"  ^  ^''"'"''  ^"  '''''''  ^  "ft  '^« 

D  IS  another  receiver,  opening  into  the  tube  T,  that  connects 
the  receiver  with  the  barrel.  Inside  the  receiver  is  placed  a 
bammetei-.  It  is  apparent  that  air  is  exhausted  from  D  as  well 
as  trom  R;  and,  as  the  pressure  is  removed  from  the  surface  of 
the  mercury  in  the  cup,  the  barometric  column  falls ;  so  that 
the  barometer  serves  as  a  gauge  to  indicate  the  approximation 
to  a  vacuum.  P^or  instance,  when  the  mercury  has  fallen  380°^ 
(15  inches),  one-half  of  the  air  has  been  removed. 

QUESTIONS. 

1.  Why  is  it  difflcnlt  for  a  person  to  lift  the  receiver  from  the  nnmn 
after  the  air  is  exhausted  from  it  ?  ^     ^ 

2.  Why  is  it  easily  raised  before  the  air  is  exhausted  ? 

3.  Suppose  tliat  the  air  in  the  pump-barrel,  when  the  piston  is  raised 
is  one-eighth  of  all  the  air  in  the  pump,  including  the  ^r  in  the  rece  v- 

4    w.  r'"'"  "'  '^''  "''' ''  •'•^'"^^'^^  "^y  "»«  «rst  double  stroke? 

4.  What  portion  of  the  original  amount  of  air  is  removed  at  the 
second  double  stroke?  ^cmuvea  ai  tne 

5.  Which  double  stroke  removes  the  most  air  ? 

6.  If  there  were  no  force  required  to  lift  the  valve  t,  why  could  not 
a  pertect  vacuum  be  obtained  ?  ^  °' 


7 
colu 

crse 

A 
may 


i 


stitute 
in  Figi 
faucet 
lated. 
will  adj 
To  the 
means ( 
which  J 


THE  AlE-PtiMp.  50 

7.   It  Is  a  very  good  pump  that  reduces  the  M^m  ^f  .,, 

column  to  3-™.     ^hat  portion  of  the  afr  ha.  h^  '  mercurial 

■SA  9                               *'       "u  ui  me  air  has  been  removed  in  that 


1?^^ 


crse  ? 


Fig.  35. 


An  absolute  vacuum  has  nev.r  beon  flHn,-r,«i      ^,     ,. 

may  be  readily  understood.     IcccMr.  to  t  T      '""'"^'^ 

Accoiaing  to  the  most  recent  cjii- 

^"•'^t'ons,  the  number  of  molecules 
contained  in  a  cubic  centimeter 
of  air  of  ordinary  density  is  some- 
thmg  like   21,000,000,000,000,. 
000,000  (twenty-one  million  tril- 
lion) ;   consequently,  when   it  is 
reduced  to  one-millionth  its   us- 
ual density,  21,000,000,000,000 
(twenty-one    trillion)    molecules 
are   still  left.     The   exhaustion 
may  be  carried  much  farther  than 
'>y  purely  mechanical  means,  by 
lieating  a  piece  of  charcoal   in 
tlie  receiver  while  the  pumping  is 
going  on.     Heat  expels  the  air 
in  its   pores.     After  the  pump- 
ing   bus    ceased,     the    charcoal 
IS    allowed    to    cool,    when     it 
condenses    a    large    portion    of 
the  remaining  air  in   its   pores. 
(See  §  37.) 

stitnfo  fx,.         •  ^  ^^^'^'  ^^^^P  ^"^^  efficient  sub- 

in  figure  86,  m  wh.ch  a  is  a,; .  i^vated  tank  of  water  iiavin..  a 
fau^t  *  by  which  the  rapid,.,  .;  the  flow  of  water  may  be  ":„! 
lated.    The  tube  o  should  be  as  long  ,«  the  hight  of'the    oom 

lo  the  end  of  the  branch-pipe  e  there  mav  be  connected  bv 
m  a„s  of  rnbber  tubing  k,  a  f  iass  tnbe  leading  to  a  vesse  7^0™ 
rtich  air  is  to  be  exha«s..u.    Water  fallhrg  freel/Ihroi^ha 


*  hIHiI 

t    'jS 


60 


DYNAMICS. 


f 


Fig.  36. 


vertical  tube  ei:ert8  no  lateral  pressure ;  consequently  there  is 
no  tendency  to  enter  the  branch  e.  As  the  v.iiej  ui  xalling 
increases  in  velocity,  it  tends  to  separate,  leaving  between  the 
cylinders  of  water  vacuous  spaces.  The  lower  end  of  the  pipe  c 
being  immersed  in  vater,  air  cannot  enter  there  ; 
but  the  air  in  the  recaiver  g  expands  and  rushes 
through  the  tube  e,  to  fill  these  vacua,  and  thu^ 
exhaustion  is  eft  jOuCd.  In  Sprengcl's  air-pump 
mercury  is  substitutt  d  for  water,  and  air  is  reduced 
by  it  to  less  than  one-millionth  its  usual  density. 

< 

Experiment  1.  Take  a  glass  tube  (Fig.  36),  having 
a  bulb  blown  at  one  end.  Nearly  fill  it  with  watei ,  so 
that  when  inverted  there  will  be  only  a  bubble  of  air  in 
the  bulb.  Insert  the  open  eiul  in  a  glass  of  water,  plr';e  under  a 
receiver  and  eximust.  What  happens?  Why?  What  will  happen 
when  the  air  is  admitted  to  the  receiver? 

Experiment  2.  Through  a  cork  of  a  tightly-stopped  bottle  pass  one 
arm  of  a  U-shaped  glass  tube  C  (Fig.  ;57). 

Introduce  the  other  arm  into  the  empty    Fig.  37. 

vessel  B.     Place  the  whole  under  a  glass 
receiver,  and  exhaust  the  air.   What ;  '  ,> 
nomena  will  occur?    What  will  hapi.  i 
when  air  is  admitted  to  the  receiver? 


§  50.  Marlotte's  Law.  —  The 
experiment  illustrated  by  Figure  32 
showed  that  the  volume  of  a  given 
body  of  gas  depends  upon  tlie  pros- 
sure  to  w)iieii  it  is  subjected.     To 

find  more  exactly  the  relation  between  tliese  quantities,  proceed 
as  follows :  — 

Experiment  1.  Take  a  bent  glass  tube  CFig.  381.  the  short  arm 
being  closed,  and  the  long  arm,  which  should  be  at  least  SSe™  long, 
being  open  at  the  top.  Pour  mercury  into  the  tube  till  the  surfaces  in 
the  two  arms  stand  at  zero.  Now  the  surface  in  the  long  arm  supports 
the  weight  of  an  atmosphere,     i'herefore  the  tension  of  the  air  en- 


do 
poi 
sur 
red 


striiif 
cury 
6.  A 
thefli 
oury  : 
atmos 
inche! 
the  16 


mariotte's  law. 


61 


}re  IS 
.Uino: 


der  a 

ippen 

s  one 


3eed 


arm 

oiig, 

s  in 

orts 

en- 


Fig.  38. 


Indstn  h  arm  whieh  exactly  balances  It,  must  be  about  15 

pounds  to  the  square  mch.    Next  pour  ni.rcury  into  the  long  arm  till  the 
surface  m  the  short  arm  reaches  5,  or  till  the  volume  of  air  enc lo  ed  is 
reduced  one-half,  when  it  will  be  found  that  the  hlght  of  the  columnl  C 
is  just  equal  to  the  hight  of  the  barometric  column 
at  the  time  tlie  experiment  is  performed.     It  now 
appears  that  the  tension  of  the  air  in  A  B  balances 
tlic  atmospheric  i)ressure, ,     s  a  column  of  ujercury 
A  C,  which  is  equal  to  anotlar  atmosphere;  .-.  the 
tension  of  the  air  in  A  B  =-  two  atmospheres.     But 
the  air  has  been  compressed  into  half  the  space  it 
formerly  occupied,  and  is,  consequently,  twice  as 
dense.     If  the  length  and  strengtli  of  the  tube 
would  admit  of  a  column  of  mercury  above  the 
surface  in  the  short  arm  equal  to  twice  A  C,  the 
air  would    be    compressed    into 
one-third  its  original  bulk ;  and, 
inasmuch  as  it  would  balance  a 
pressure  of  iliree  atmospheres,  it- 
ten'^  ion  would  be  increased  throt- 

1       erlment  2.    Next  take    a 
glass  tube  (Fig.  39)  open  at  l)oth 
ends,  and  about  24  inches  long. 
Tie  three  strings  around  the  tube, 
—  one   3   inches   from    the    top, 
another  6  inches,  and  the  third  21 
inches..   Nearly  fill  a  glass  jar,  B, 
25    inches    high   with    mercury. 
Lower  the  tube  into  the  mercury 
till    it    reaches  the  string  at  3. 
Press  a  finger  flmly  over  the  up- 
per end,  and  raise  the  tube  till  the 
string  at  21  is  on  a  level  with  the  surface  of  the  mer- 
cury in  tl  '  jar.     The  mercury  in  the  tube  will  stand  at 
6.    At  first  the  air  enclosed  in  the  tube  between  8  and 
the  finger  withstands  an  upward  pressure  of  the  mer- 
cnrj'  suffic    =:t  to  sustain  a  column  of  i,,.  rcury  SO  inches  high,  or  one 
atmosphere.    When  the  tube  is  raised  and  the  mercurv  stands  at  6   15 
inches  high,  one-half  of  that  upward  pressure  is  exerted  in  sustaining 
the  16  Inches  of  mercar5^  and  the  other  half  is  exerted  on  the  enclosed 


^:l' 


(52 

DYNAMICS. 

lated  as  f„lto„»'-  '""  ""'  °'  "^P"l>nents  may  be  tabu- 

Pressure   ....  i    j    i    «    „    . 

Volume     .     .  •    •    I't'^'^'^^- 

Density     .  '     '     '         i    ,''  ^'  *'  ^'  '^^■ 

Elastic  force'    :;■••''     '  ?'  .^'  ,*'  ^<^- 
3.  i.  1,  2,  3,  4,  &c. 

From  tlK..„.  results  we  learu  that,  at  twice  the  pressure  th„„ 

.  s  a"'"Ar;::rtr''"'  '"^  ^-^''^  -"  »'»*  ~ 

uistovuul  It  at  about  tlic  same  time.     This  law  i,  tn.n  f^- 

»n  gases  w.thiu  certa mits,  hut  under  e.treuV  or  ,s ,  e  tt 

-  -^on  ,„  volume  is  greater  than  iudieatecl  ,,;,"     ^V  "tt 
;|- ..>t™  from  ,t  occurs  with  those  gases  tha't  are  mos't  Ltty 

QUESTIONS. 

1.   Into  the  neck  of  a  bottle  partly  fllle,!  with  water  (Fig.  40)    in- 

^'^-  40-  t^h/  '°?  "''^  "^""^'  ""•'^"^'"  ^^''"'^l'  P'»««««  «  glass 

tube  nearly  to  the  bottom  of  the  bottle.     Blow  forci- 
bly into  the  bottle.    On  removing  the  mouth,  water 
will  flow  through  the  tube  in  a  stream.     Why? 
2.   How  can  an  ounce  of  air, 

in  a  closed  fragile  vessel,  sus-    FiJ?.  41. 

tain  the  outside  pressure  of 
the  atmosphere,  amounting  to 
liH^^H    ^'^evcral  tons? 

3.   What  drives  the  peljots 

from  a  pop-gun  ? 

Ilg^_       4.    I'lgure  41  represents   a 

dropping-bottle,  much  used  in 

chemical  laboratories.      Why 

do  bubbles  of  air  force  their 

way  down  into  the  liquid?  -     '       "'  ■»iia^ 

^^  stop  the  upper  ormce,  .„a  .he  U,„.a  ^  ,„,„y,  ^^  ^  ^^^ 


9.   S 


contracti 
44),  int< 
condense: 


>p. 


Flgr.  42. 


CONDENSER.  go 

IS  just  below  the  surface  of  the  boiling  liquid  As 
the  water  evaporates,  and  its  surface  falls  below  the 
mouth  of  the  bottle,  an  air-bubble  enters  the  bottle 
expands,  and  pushes  out  enough  water  to  cover  once 
more  the  mouth  of  the  bottle.  Why  does  not  the  air 
push  out  all  the  water  from  the  bottle? 

7.  Fi^-'ure  43  represents  a  weight-lifter.  Into  a 
hollow  cylinder  s  is  fitted  air-tight  a  piston  t.  The 
cylinder  is  connected  with  an  air-pump  byarubi)er 
tube  n.  When  air  is  exhausted  the  piston  rises  lift- 
lug  th<' heavy  weight  attached  to  it.     Why? 

onnt  V  ^''l'"''"'  "^  ^^"^  ''''''''■  '"'■'■^^^  «f  the  piston  is 
2010™,  how  heavy  a  weight  ought  to  be  lifted  when 
the  air  is  one-lialf  exhausted  ? 
9.   Suppose  you  tightly  stopper  a  bottle  at  the  top  of  Mont  Bianc,  car- 

ry  it  to  the  sea-leveJ. 
insert  the  mouth  of 
tlie  bottle  in  water, 
iiiid  withdraw  the 
stopper;  what  would 
happen  ? 

10.  Show  that  the 
labor  of  working  the 
kind  of  air-i)nmp  de- 
scribed (§  4l>)  increas- 
es as  the  exhaustion 
progresses. 


Fig.  43. 


§  51.  Condenser. 
—  Ill  the  experi- 
ment with  the  bottle 
(Fig.  40),  air  was 
condensed  in  the 
mouth  by  muscular 
contraction  and  forced  intx>  the  bottle.  An  apparatus  A  (Fie 
44)  uitended  to  condense  air  in  a  closed  vessel,  is  called  "a 
condenser.     Its  constructi,  a  is  like  that  of  the  barrel  of  the 


ff 


64 


DYNAMICS. 


air-pump,  except  that  the  position  of  the  valves  is  reversed. 
(Compare  with  Fig.  34.)  What  differences  do  you  notice  in 
respect  to   the   valves?     What   happens   to 

the  valves  when  the  piston  in  the  condenser    ^^^'*^' 

is  forced  down?  If  the  condenser  is  con- 
nected with  a  closed  vessel  B,  how  much 
iiir  would  be  forced  into  it  at  one  down 
stroke?  VVHiat  prevents  the  air  from  o.s 
eaping  during  an  up  stroke?  If,  after  air  is 
condensed  in  B,  the  cylinder  C  is  connected 
witli  it  by  a  screw,  and  the  stop-cock  t  is 
suddenly  turned,  what  would  happen  to  the 
bullet  .s  ?  Wliat  name  would  you  give  to  such 
"n  apparatus? 

The  Western  Union  Tclosraph  Company,  in 
V'w  York  City,  employs  atmospheric  pressure  in 
forwardinj?  messages  to  its  central  olHce  from 

frnr^lT?  ''^"^''^'^'  '*^"^"'  "'  '^"''  '''^'-    '^"^'^^  «f  ""'form  siso,  free 
from  sudden  em-vatures,  and  laid  under  ground,  connect  the  bmuch 

on  ces  with  headquarters.  Rolls  of  paper,  or  lettc  -s  to  be  des- 
patched, arc  deposited  m  a  cylindrical  box  c  (Fig  45)  whieli 
fits  the  interior  of  Mie  tube.     The  box  being  dropped  into  the 

6^  end  of  the  tube 

at  a,  and  the  air 
being  exhausted 
from  tlie  tube  at 
the  end  h,  by 
^^^i^X^^'^^M  ^^^^^'^^^P     means  of  an  air- 

Steam,  air  rushes 

, ,     , ™ -  -.^--  -- .--V .  «!^*>^5^^-s^!s^w5^ss»ss5^5%.^x^^     in  at  a  and  pushes 

I"  l>ox  tiirough  the  tube  with  a  foree  of  several  pounds  for  every  square 
i.c  .  of  the  end  of  the  box.    The  operation  is  still  further  facilitated 
riy  tJie  aid  of  a  condensing-punip  worked  by  steam  at  the  end  a. 

§  52.  Pressure  transmitted  undiminished  in  all  direc- 
tions. -  Fill  the  globe  G  (Fig.  4.1) ,  and  about  one-fifth  t  lu-  ..ylin- 
dor  C,  with  water.   The  water  in  the  tubes  a,  b,  c,  and  d,  will  rise 


Fig.  45. 


! 


PRESSFHE    Tl; ANS.M ITTED. 


65 


to  the  same  level  wit!,  the  water  in  the  cvliuck-r  C.  N<nv  Ibree 
the  pisto.i  !•  into  the  cylinder,  and  the  downward  pres.sure  will 
^'UMse  ,,et8  of  water  to  issue  from  eacl,  of  the  tubes.  But  the 
s  rounds  from  the  tubes  «,  6,  and  c,  rise  t«  exactly  the  same 
hight  that  the  stream  fro.^.  the  tube  d  does,  although  the  li(,uid 
Fig.  46.  ia  the  latter  tube   re- 

ceives the  direct  ac- 
tion of  the  downward 
force.  It  thus  ai)pears 
tliat  the  pressure  is  not 
felt  alone  by  that  por- 
tion of  the  liquid  that 
lies  in  the  path  of  the 
force,  but  is  folt  equally 
iu  all  parts  and  in  all 
directions. 

If  the  globe  is  filled 
with  air,  and  subjected 
to  pressure  as  aK.uv'e, 
eurrents  of  air  will  is- 
sue from  the  several 
tubes  with  equal  force. 
This  i)roperty  of  trans- 
mitting pressure  equal- 
ly in  all  directions, 
which  IS  peculiar  to  fluids,  is  due  to  their  viobility  and  i»'rfeci  ' 
elasticity. 

Figure  47  represents  a  number  of  elastic  hooi)s  enclosed  iu 
the  vessel  AIU'D.  A  weight,  plaee.l  on  a,  communicates  to 
It  a  downward  pressure.  It  is  evident,  that  not  only  is  the 
pressure  communicated  to  the  hoops  below  it  in  succession,  and 
finally  to  tl.e  h^MUm  of  the  box,  but  there  is  also  a  lateral  pres- 
sure due  to  th('  elastic  property  of  the  hoops.  The  hoop  (;, 
receiving  pressure  fio.ii  b,  above,  reacts,  exerting  an  upward 
pressure  ;  it  also  prosses  laterally  upou  the  side  A,  and  the  hoop 


'  HrJNil 


<'m 


m 


66 


DYNAMICS. 


>V- 


nl  „i„"  7'"' "'"  """r'"'^ """" "'''"'"  -1  "■«"''- 

iiius,    upward,    downward,    and 

laterally,   a  force  equal  to  the    "^  ''' 

dovvuward  pressure  of  the  weight 

W.     Hence  that  portion  of  the 

bottom   Ininiediatcly    under  the 

weight  receives  no  greater  pres- 

sure  from  W  tlian  an  equal  area 

of  any  otiier  part  of  the  bottom, 
or  than  an  ecpial  area  of  either 
of  the  sides,  A  and  B,  or  the  top 
C.  This  operation  illustrates, 
somewhat  imperfectly,  the  meth- 
od by  which  elastic  fhiids  traus- 
nnt  pressure  uuthminished  in  all 
directions, 

if  we  take  a  quantity  of  water 
!"  ^  ''«^««I  A   i^\-    48),   shut   ^^^^m 

1^-  a^d^^rtd  .:;  "'  ^k  ^'^^    ^^-^^^^    ^^-   -«P-tiveIy 

;'-atte;isn:rirt:^;rr\^^^ 

former,  but  that  it  will  require  a  -l,)-gram 
;7;P'''^^-^ ---to  preserve  equilihHm" 

nt  te  area  of  the  piston  i  is  4.....    ,vhile 

Ik.  piston  a  contains  four  such  areas- 
hence  It  follows  that  a  pressure  of  10«  is 
transmitted  to  each  of  the  4-  of  a,  and  lust 
supports  the  40-gram  weight.  Had  the  am! 
of  the  piston  b  been  1-.-,  then  the  10-gram 

weight  ph.ced  on  it  would  require  a  1  GO  gram ^— 

weight  placed  on  a  to  balance  it  •  t Lf  ^ 

would  be  exerted  on  eve^  .quare^:  ^^^  ;,  f^^^  ^'  ''' 

Obviou.1,  UU«  for.  or  apparatus  cannot  ..  ....Uo  to  woric  well  on 


Fie.  48. 


'e  to 
aus- 


at 


HYDROSTATIC  BELLOWS   AXD   PRESS.  67 

'  account  of  the  friction  of  the  pistons-   hnf 

the  pistons  and  weights  colum.fs  of  m'  .  ^^  ""'"^  «nbstitute  for 
-nncctiug  tube  and^the  lon-Tplt  of  ?h  h'  ^^  '"'''"'''  '''  ^"« 
cury;  the  two  free  surfaces  wiU  t  tt  sT  ?"  f""'  "'">  '"^'- 
of  any  liquui,  e.rj.  water    is  no.nwi      .     i         ^'^  ^''^''^-     ^'''^  ^f  108 

§  53.   Hydrostatic  bellows  —  Ti.;.  .   •     •  ,     . 

tal;.!,''""'''''^'''^^'^^^^thcr  at- 
tached to  then-  edges,  as  to  form  an  air- 
tiglit  vessel  called  tlie  bellows.     A  <.lass 
t'lbe  a,  having  a  bore  of  l-i-.  sertion' 
communicates  with  the  interior  of  the  bel' 

ows      Let  water  be  ponred  into  the  tube 

^  til  the  boards,  is  raised  a  few  centime- 

tei.     The  water  wilUtand  at  the  same 

.m  the  tube  and  bellows.     Now,  if 

oO«  of  ,,,tcr  be  poured  into  the  tube,  it 
H.Il  requn-e  a  weight  of  20,000«  to   be 

placed  upon  6  to  prevent  its  rising.     Any 

the  oO«  of  water      ,f  ^n^fl   T'  """  '''''  "'"  '^  ^'^'^-^  '>y 
i>eIlows,  a  Teton    t..  /   ""TZ  ''^'"^  '"^'•'^''--^  '"^>  the 

eaaii,raise\.m:^t^ni:^^:;i^t::ir '-'  ^"^^'  '^^  -" 

na.e  Of  the  inventor.     You  see  t::;i;i::nXFS::  JIT 


Ml 

£     1 

Ik 


Mi' 


i 


m 


DYXAMrcS. 


m^.  50, 


The  area  of  the  lower  surface  of  t  is  (say)  one  hundred  times 

that  of  the  lower  surface  of  s.     As  the  piston  s  is  raised  and 

depressed,  water  is  pumped  up  from  the  cistern  A,  forced  into 

the  cylinder  x,  and  exerts 

an     upward     pressure 

against  tlie  piston  t  one 

luindred     times     greater 

than  the  downward  pres- 
sure   exerted     upon     s. 

Thus,  if  a  pressure  of  one 

hundred  pounds  is  applied 

at  s,  the  cotton  bales  will 

be  subjected  to  a  pressure 
of  five  tons. 

The  pressure  that  may 

be  exerted  by  these  press- 
es is  enormous.  The  hand 
of  a  child  can  break  a 
strong  iron  bar.  But  observe  that,  although  the  pressure  ex- 
erted is  very  great,  the  upward  movement  of  the  piston  t  is 
very  slow.  In  order  that  the  piston  t  may  rise  P-",  the  piston  s 
must  descend  100-'.  The  disadvantage  arising  from  sic  .mess  of 
operation  is  little  thought  of,  however,  when  we  consider  the 
great  advantage  accruing  from  the  fact  that  one  man  can  pro- 
duce as  great  a  pressure  with  the  press  as  a  hundred  men  can 
exert  without  it. 

Tlie  press  is  used  for  compressing  cotton,  hay,  etc.,  into  bales, 
and  for  extracting  oil  from  seeds.  The  modern  engineer  finds 
it  a  most  efficient  ma(!hine.  whenever  great  weights  are  to  be 
moved  through  short  distances,  as  in  launching  the  Great  East- 
ern steamship. 


§  55.   Pressure  in  fluids  diiA  +.n  o-ratri+w  ._  tr 


rtViH?  con  - 


sidored  the  transmission  to  the  walls  of  the  containing  vessel,  of 
external  pressure  applied  to  any  portion  of  a  surface  of  a  liquid, 


i>KESSUKE  IN  FLUIDS  DUE  TO  GRAVITY. 


GO 


Fig.  51. 


we  MM  examine  the  effects  of  pressure  due  to  the  weight  of  the 
liquids  themselves.     Suppose  that  we  have  three  vessels  filled 

with  water,  A,  B, 
andC  (Fig.  51),  of 
equal    depth,    and 
liaving  bottoms  of 
equal  areas.     It  is 
plain  that  the  bot- 
tom of  vessel  A  sus- 
tains a  pressure  equal  to  the  weight  of  the  column  of  water 
abed,  or  just  the  weight  of  the  water  in  the  vessel.     The  pres- 
sure on  /y,  a  portion  of  the  bottom  of  vessel  B,  is  equal  to  the 
weight  of  a  column  of  water  ghji.     But  this  pressure  is  trans- 
mitted   undiminished   to   the   surface   fh;    consequently,   the 
pressure  on//t  is  equal  to  the  weight  of  a  column  of  water  of 
the  size  of  ef/,g,  and  the  pressure  on  ^7  is  equal  to  the  weight  of 
a  column  ijlk.     Hence  the  pressure  on  the  whole  bottom  fl  is 
equal  to  the  pressure  of  a  column  of  water  eflk,  or  the  same 
as  the  pressure  on  the  bottom  of  vessel  A.     But  the  weight  of 
the  water  in  B  is  less  than  the  weight  of  the  water  in  A.      Hence, 
(1)  the  pressure  on  the  bottom  of  a  vessel  may  be  greater  than  the 
weight  of  the  water  in  the  vessel. 

In  vessel  C,  the  side  mq  sustains  the  downward  pressure  of 
the  body  of  water  mqn;  and  the  side  pr  sustains  the  pressure  of 
the  body  orp;  while  the  bottom  r/r  sustains  only  the  pressure 
of  the  column  nqro,  which  is  equal  to  the  pressure  on  the  bot- 
toms of  each  of  the  vessels,  A  and  B.  Hence,  (2)  the  pressure 
on  the  bottom  of  a  vessel  may  be  less  than  the  weight  of  the  water 
in  the  vessel. 

We  conclude,  therefore,  that  (.3)  the  pressure  on  the  bottom 
of  a  vessel  depends  on  the  depth  and  area  of  the  bottom  and 
the  density  of  the  liquid,  and  is  independent  of  the  shape  of  the 
vessel  and  ike  quantity  of  liquid.  -The  important  fact  that  the 
pressure  on  the  bottom  does  not  depend  on  the  shape  of  the 
vessel  is  often  called  the  hydrostatic  paradox,  beeauae,  though 
true,  it  aeems  at  first  absuYd. 


i 


70 


tnrsAMum. 


rrj;ir  ^'"^'  -  "--^  i."urr  r^ir;; 

««ch.    Etuih  vernal,    m^^^^  "'  " 

when  Id  UPC  1h  sup- 
ported by  the  tripod 
"•    The  dl«k  is  sup 
ported  and  presst-d 
up  «tron«;ly  against 
the  bottom  of  the 
vessel  by  means  of 
a  string  passin/if  up 
through  the  vessel, 
and  attached  to  a 
sprlng-bahince.  Let 
water  be  poured  In- 
to vessel  C,  and  reg. 
ulate  at  pleasure  the 
amount  of  down- 
ward pressure  nec- 
essary to  push  the 
bottom  off  and  al- 
low the  water  to 
«8cape.     Note  the 
depth    of    water 
when  the  bottom  IS  ,^,^^^^^^^^^^^^^^ 

^^^'"^^'^^^^  -Ubth.  pointer/.     Also 

vessel  A  for  vessel  O.     PourL  l!!i  .  *"'  ''*'«'^«'    Substitute 

bottom  will  be  forced  off  at  U^^  ^J.'Zf  ,  ""^"**'''  •^'  ^'"^"  ".e 

pointer,  and  by  the  same  pn!..^!  '  ^  'f ^^^  ^  *""^^"  ''^  the 
But  much  less  wat«r  is  re.u^Xn  Tj  '7  '^  *'"'  •»l'r»"«-balanoe. 
experiment,  repeated  wfU^eCl  ?  wTu.'  *1.'''"'  ""'  *'^-"''*"  '^  ''"« 
ase  of  a  stlU  Urn  qaantHy  of  waL!r         *  ••**^'  ''^*«'^  ^1"'  ".e 

-v?^  ,.  j^  ^^-^  ^  _   ^^        northern  ,  f  ,t.     1  '   '-' ^VW^S  srnose 


QUESTIUNS  AND  PKOBLEMS.  7^ 

suppose  the  area  of  hj,  of  the  bottom  of  vessel  R  ^'Fi*,   k^\    • 

JOO  .  And,  since  the  weight  of  one  cubic  centimeter  of  water 
IS  one  gram,  the  weight  of  the  column  is  900«,  which  il  the 
pressure  on  the  surface  /,•;  and  the  pressure  on  eac  o  i'e 
equal  surfaces  //.  and  jl  being  the  same  as  on  /y,  the  pressure 
on  the  entire  bottom  is  2700«.  pressuie 

Evidently  the  lateral  pressure  at  any  point  of  the  side  of  a 
vesse,  depends  upon  the  depth  of  that  point;  and,  as  depth 
at  different  points  of  a  side  varies,  hencc^S)  o  find  t~ 
sure  upon  an,  portion  of  a  side  of  a  vessel,  IJftncUke  Jig  t  of 
a  column  of  r.ater  rohose  base  is  the  area  of  that  portion  of  Z 
^,ana  .hose  hight  is  the  average  depth  Jtha,  pZ^^^  tC 
we  compute  the  pressure  on  the  side  ah  of  vessel  A  (Fig  51) 
n-  multiplying  the  area  of  the  side  90-  (dimensions,  9  x  10-' 

of  I      ot  water,  which  gives  405«  for  the  pressure  on  the  sUie 
QUESTIONS  AND   PROBLEMS 

bottom.    How  rapidly  should  its  thickness 
increase  ? 

2.  At  high  tide,  suppose  the  flood-gate  of 
a  dock  to  be  closed,  leaving  the  surface  of 
water  on  the  inside  and  outside  of  the  gate 
at  the  samo  lovel.  From  which  does  the  gate 
siistaiu  the  {rreater  pressure,  the  water  in 
I  lie  dock,  or  the  ocean  of  water  outside? 
Why  ' 

„. ,  ,  ,^  ®-  "^^^  interior  dimensions  of  the  rectan- 

depth.    Tiie  vessel  is  full  of  water.     Hnmnu*..  fKo  *of«>  -r^«„^ 
each  of  the  six  sides.  """"   "  ''°*^'  ^'^'^"^  °° 

i«  L^"?r  ""'^  '^'  P'"^  "  ^^'^-  ^*>'  *^«  ^f«*  «f  whose  end  is  4aem. 

what  ;!TrH     T  '"""  ''''  ''"'''''  "'  "'«  ^'**«'-  ^'^»^  the  force  of  100. 
what  additional  pressure  will  each  side  of  the  vessel  sustain  ? 


Fig.  53. 


H  ^ 


72 


DYNAMICS. 


6.    How  great  will  be  the  whole  pressure  that  each  side  sustains, 
due  to  the  weight  of  the  liquid  and  the  external  pressure? 

6.  Suppose  mercury,  which  is  13.6  times  heavier 

than  water,  to  be  employed  instead  of  water,  what    '^^  ''*• 

would  be  the  answers  to  the  three  preceding  ques- 
tions? 

7.  Into  the  top  of  a  keg  filled  with  water,  a  brass 
tube  lom  long  is  inserted,  a  transverse  section  of 
whose  bore  is  l-icm.  Tlie  depth  of  the  water  in  the 
cask  is  30'=™,  and  the  area  of  the  bottom  of  the  cask 
is  40iem.  (a)  Compute  the  pressure  on  the  bottom  of  the  kes 
(6)  Compute  the  pressure  on  the  bottom  of  the  cask  if  the  tube  is  filled 
with  water,  (c)  What  is  the  weight  of  the  water  in  the  tube  that 
causes  this  extra  pressure? 

8.  What  crushing-force  on  each  side  would  an  empty  cubical  box 
tiie  area  of  one  of  whose  sides  is  li™,  sustain,  if  lowered  l^m  into  the 

9.  What  crushing-force  on  each  side  would  this  box  sustain  from 
the  atmospheric  pressure  at  the  sea-level,  if  the  air  were  completely 
exhausted  therefrom?  i'lcieiy 

10.  Suppose  the  top  of  the  vessel  (Fig.  54)  to  be  the  weak  part  of 
the  vessel,  not  able  to  sustain  more  than  508  pressure  on  10«<=™  what 
pressure  applied  to  the  plug  will  burst  the  vessel? 

§  56.  The  surface  of  a  liquid  at  rest  is  level.  —By  jolt- 
ing a  vessel  the  surface  of  a  liquid  in  it  may  be  made  to  assume 
the  form  seen  in  Figure  55.     Can  it  retain  this  form  ?    Take 
two  molecules  of  the  liquid  at  the  points  a 
and  6,  on  the  same  horizontal   level.     The 
downward  pressure  upon  a  is  the  weight  of 
a  column  of  molecules  ac,  and  the  downward 
pressure  upon  b  is  the  weight  of  the  column 
bd.     Now,  since  the  pressure  at  a  given  depth 
is  equal  in  all  directions,  bd  and  ac  represent 
the  lateral  pressures  at  the  points  b  and  a  respectively.     But  bd 
IS  greater  than  ac ;  hence,  the  molecules  a  and  6,  and  those  lying 
m  a  straight  line  between  them,  are  &ot^A  nnnn  u.r  fw«  ..^l„^^ 
forces  m  opposite  directions.     There  will,  therefore,  be  a  move- 
ment of  molecules  in  the  direction  of  the  greater  force  toward 


Fig.  55. 


I 


ARTESIAN   WELLS,   ETC.  73 

a,  tUl  there  is  equilibrium  of  forces,  which  will  only  occur  when 
the  points  a  and  b  are  equally  distant  from  the  surface  ;  or  in 
other  words,  there  will  be  no  rest  till  all  points  in  the  surface  'are 
on  the  same  horizontal  level. 

This  fact  is  commouly  expressed  thus:   "Water  always  seeks  its 
owest  level."    In  accordance  with  this  principle,  water  flows  down  an 

a^i"Ition"f'H  ""'  "?  "™""  ^"^P^^  "P-  ""-  "^-*-tion  oTtho 
a,  phcat  on  of  this  pruic.ple,  on  a  large  scale,  is  found  in  the  method 
.supplyu.g  cities  with  water.  Figure  5G  represents  a  modern  a  que- 
duct,  through  which  water  is  conveyed  from  an  elevated  pond  or  river 

Tn  a'c'lt'v  ;/  'T-  t'  "'"  "  ^""  ''  "^"-^"^^  ^  -"^y  ^'  '-  '  '--vo^" 
m  a  city,  from  which  water  is  distributed  by  service-pipes  to  the  dweu' 

Fig.  56. 


lugs.  The  pipe  is  tapped  at  different  points,  and  fountains  rise  theo- 
retically to  the  level  of  the  water  in  the  pond,  but  practically  not  so 
high,  on  account  of  the  resistance  of  the  air  and  the  check  which  the 
ascending  stream  receives  from  the  falling  drops.  Where  should  the 
pipes  be  made  stronger,  on  a  hill  or  in  a  valley?  Where  will  water 
issue  from  faucets  with  greater  force,  in  a  chamber  or  in  a  basement? 
How  high  may  water  be  drawn  from  the  pipe  in  the  house/? 

§57.  Artesian  wells,  etc. -In  most  places,  the  crust  of  the 
earth  is  composed  of  distinct  layers  of  earth  and  rock  of  various  kinds 
These  layers  frequently  assume  concave  shapes,  so  as  to  resemble  oups 
placed  one  within  another.  Figure  57  represents  a  vertical  section 
exposing  a  few  of  the  surface-layers  of  the  earth's  crust :  a  is  a  stratum 
of  loose  sand  or  gravel;  b,  a  clay-bed;  c,  a  stratum  of  slate;  d  a 
stratum  of  limestone ;  the  whole  resting  on  a  bed  nf  jrranH»  .  if  ,,«., 
hoUow  out  a  lump  of  clay,  and  pour  water  into  the  cavitv,  you  will 
find  that  the  water  will  percolate  through  tlie  clay  very  sl'>wi  Water 
tliat  falls  in  rain  passes  readily  through  the  gravel  a,  till  U  •  l.-hes  thf 
clay-bed  6,  where  it  coUects.    Hence  a  well,  sunk  to  the  cl    --bed,  wlU 


^J: 


m 


74 


DYNAMICS. 


Fig.  57. 


Pig.  59. 


a  p.1.0  tiuougl,  a  .like  by  tl,.  seashore,  and  c,n-ve  it  „  wari    ho 

r:,r;r  :;';;f '■  '^""  '"^  --'-■•  -  --i^  '^e  pi: 

Notwithstanding     that     every-day 
experience  teaches  that  "  liquids  seek 
a  level,"   it    may  soem  strange  tliat 
the   If.rge    quantity     of    water  in    a 
teapot    is    balanced    by     the    small 
quantity   in  the  nozzle.      Why,    for 
inst.ance,    should   the   liquid    in   the 
small  arm    B    balance  the    liquid  in 
the  large  arm  A,  of   the    vessel    in 
.     1       ,.  ^''^'  ^^'-      Imagine  the   liouid  in   A 

columa  e.     It  is  dear  that  the  downward    pressure  ot  any 


one 
ward 
is  nc 
othei 


r^ 


§59. 

f erring 
of  atmo 


SIPHONS. 


76 


one  of  the  columns  a,  b,  o,  d,  or  e,  will  balance  the  down- 
ward  pressun.  of  anyone  of  the  other  COJU..US,  and  that  there 
.8  no  reason  wh^.  e  should  rise  above  any  one,  or  all,  of  the 


.  o9.  Siphon.  -  A  siphou  is  a  an  instrnment  used  for  trans- 
fernncr  a  hqmd  from  one  vessel  to  anothei-  through  the  acreucv 
Of  atmospheric  pressure.     It  consists  of  a  tube  of  any  material 


^f^f- 


IMAGE  EVALUATION 
TEST  TARGET  (MT-S) 


4- 


m/^ 


4- 


Cj?/ 


A 


f/. 


1.0 

=^  !?  ■**  l-^.^ 

e:  i^  ^ 

I.I 

Hut. 

lllll^^ 

m 

1.25 

U.      1.6 

^ . 

6"     • 

Til 4 U- •_ 

rlluuj^-dpiuu 

Sciences 
Corporation 


23  WEST  MAIN  STREET 

WEBSTER,  N.Y.  14580 

(716)  872-4503 


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76 


DYNAl^IJCS. 


mbber  IS  often  most  convenient) ,  bent  into  a  shape  somewhat 

.qud,  stop  each  end  with  a  finger  or  cork,  insert  one  end  in 
the  hqu,d  to  be  transferred,  bring  the  other  end  below  the  lev.I 
of  he  surface  of  the  liquid,  remove  the  stoppers,  and  the  liquid 
;v.l  .mmeduately  flow.  What  are  the  forces  acting  on  the  wat  r 
•n  the  siphon  A  (Fig.  59)  F  What  forces  tond'to  move  th" 
water  ft-om  the  tall  jar  to  the  short  one?  What  forces  tend  to 
move  the  water  the  other  way  ?  By  how  much  does  the  one  set 
of  forces  exceed  the  other?    When  will  the  water  cease  to  flow? 

tall  jars  or  bottles,  experiment  with  it  as  in  B  and  C.    State  and 
explaira  the  results  of  your  experiments. 

The  remaining  diagrams  in  this  cut  represent  some  of  the 
great  variety  of  uses  to  which  the  siphon  may  be  put      D   F 
and  F  are  different  forms  of  siphon  fountains,  'in  D    the 
s.phon  lube  is  filled   b^  blowing  in  the  tube  /.     Explai^  the 
remamder  of    the  operation.       A  siphon  of   tie  form  G 
always  ready  for  use.     It  is  only  necessary  to  dip  one  end  into 
the  iq,„cl  to  be  transferred.     Why  does  the  liquid  not  fl^w  out 
of  tins   ube  in  its  present  condition?    H  illustrates  the  method 
by  which  a  heavy  liquid  may  be  removed  from  beneath  a  lighter 
vpll  •   ^  r''"'  ""^  '  "^P^^"  "  ^•'l"'^  ™^^  ^«  removed  from  a 

t^rth.  r  '  ^'^T  l""^'  A  liquid  will  not  flow  from  this  cup 
till  the  top  of  the  bend  of  the  tube  is  covered.  It  will  th^n 
contuiue  to  flow  as  long  as  the  end  of  the  tube  is  in  the  liquid. 
The  siphon  J  may  be  filled  with  a  liquid  that  is  not  safe  or 
p^  asant  to  handle,  by  placing  the  end  J  in  the  liquid,  stopping 
the  end  A;  and  sucking  the  air  out  at  the  end  I  till  the  lower  end 
13  filled  with  the  liquid. 

Gases  heavier  than  air  may  be  siphoned  like  liquids.  Vessel  o 
contains  carbonic-acid  gas.  As  the  gas  is  siphoned  into  ll 
vessel  p,  It  extinguishes  a  candle-flame.  Gases  lighter  than  air 
are  siphoned  by  inverting  both  the  vessels  and  the  siphon. 


..^ 


Apparatus  fok  raising  liqujlDS. 


77 


QUESTIONS. 

1-    "What  is  the  greatest  hight  to  which  the  bend  r  (in  A,  Fig.  59) 
can  be  carried,  and  aliow  water  to  flow? 

2.    What  would  be  the  greatest  hight  if  mercury  were  used? 
3     Suppose  the  bend  r  is  IS"  above  the  liquid;  what  theoretically 
ought  to  happen  when  tlie  end  h  is  unstopped? 

4-    What  would  happen  if  the  long  arm  were  tut  ofl"  at  e  ? 
What  would  happen  if  it  were  cut  off  between  e  and  a? 
What  would  happen  if  the  siphon  were  lifted  out  of  the  liquid? 
W' at  would  be  the  effect  of  lengthening  the  long  arm? 
Must  the  two  arms  of  a  siphon  be  of  unequal  length? 
How  far  can  a  liquid  be  carried  by  a  siphon? 
Will  a  siphon  work  in  a  vacuum? 

Imagine  that  some  such  condition  of  things  as  is  represented  by 
the  apparatus  K  (Fig.  59)  exists  in  the  earth,  and  that  the  siphon  a 
has  a  smaller  bore  than  the  siphon  c;  'can  you  account  for  intermittent 
springs  which  flow  and  cease  to  flow  at  nearly  equal  intervals  of  time? 
12.  If  the  siphon  A  were  carried  to  the  top  of  a  mountain,  would 
the  water  run  through  it  more  rapidly  or'  less  rapidly,  or  at  the  same 
rate?    Your  reason  for  your  answer. 


6. 

6. 

7. 

8. 

0. 
10, 
11. 


Fig.  60. 


§  60.  Apparatus  for  raising  Liquids.  —  The  siphon  can 
only  be  used  for  transferring  liquids  over  hights  to  a  lower 
level.  Liquids  cannot  be  transferred  to  a 
higher  level  by  atmosoheric  pressure  alone.  In 
fact,  atmospheric  pressure  is  only  a  conven- 
ience, and  never  does  work.  If  the  piston  a 
ot&  syringe  (Fig.  60)  is  raised,  the  air  is  rare- 
fled  below  it,  and  the  atmospheric  pressure  will 
force  water  up  into  the  syringe ;  but  to  raise 
the  piston,  against  the  atmospheric  pressure 
tending  to  force  itdovenward,  requires  as  much 
muscular  energy  as  Would  be  required  to  raise 
the  same  quantity  of  water  to  the  same  hight  as  that  to  which 
il  is  raised  in  the  syringe. 

The  common  lifling-pump  is  constructed  like  the  barrel  of  an 
air-pump.      Figure  61   represents    the    piston  in  the  act  of 


m 


T8 


t 

.■si 

-.  i 

\  * 

\i 


i: 


II 


DYNAMICS. 


Wg.  61. 


rising.    As  the  air  is  rarefied  below  it,  water  rises  hv  ^fmr.. 
Phene  pressure,  and  opens  ..  lowe.  valVl  Ve TeigttT^^^^^ 
water  above  the  piston  closes  the  upper  valve,  and 
the  water  .s  discharged  from  the  spout.    When  the 
piston  IS  pressed  down,  the  lower  v.ive  closes, 

botto'Tf  2u  "'T'  '"'  ''''  "^^^  ^^-«^-  the 
bottom  of  the  barrel  and  the  piston  passes  through 

the  upper  valve  above   the  piston.      How  hifh 
can  the  bottom  of  the  barrel  be  above  tlie  surface 

How  high  If  it  is  mercury? 
-  ^g-  62-  '^h®  liquid  is  sometimes  said  to  be 

laised  in  a  lifting-pump  by  the  "  force 
of  suction."    Is  there  such  a  force  ? 

Experiment.    Bend  a  glass  tube  iuto 
a  U  shape,  with  unequal  arras,  as  in  Figure  G2     Ffli  rhn 
tube  with  a  liquid  to  the  level  c6      Clo^.h       II 
a  finger,  and  try  to  suck  the  '  ''''  '°^  '  ^^'^ 

liquid  out  of  the  tube.    You    .  g. 

fhP  fl.        *    ^'"^  '^  impossible.    Remove 

t^  finger  from  b,  and  you  can  suck  the 

liquid  out  with  ease.    Wliy? 

The  piston  of  a  fone-pump  (Fig. 
63)  has  no  valve,  but  a  branch  pipe 
leads  from  the  lower  part  of  the  bar- 
rel  to  an  air-condensing  chamber  a, 
ftt  the  bottom  of  which  is  a  valve  c, 
opening  upward.  As  the  piston  is 
raised,  water  is  forced  up  through  the 
valve  c?,  while  water  in  a  is  prevented  ,■ 

^roed  into  tUe  cha.t::  e!';..  :^:^;C'j'^\  " 

The  eia,tlcity  „,  t„o  condensed  ai,-  fo^s  ^  ^Z  '  !  "t/' 
hose  6  m  a  continuous  stream.  * "'  ""' 


BUOYANT  FORCE  OF  FLUIDS. 


79 


atmos- 
b  of  the 


a 


ill  the 
b  wftU 


V.    BUOYANT  FORCE  OF  FLUIDS 

less  tm  it  is  .o^^C^C^^TXxTr'^'"'  .^"'"^"^  '^^«"- 
and  note  the  change  il ZxZtti  .^Z"" T"" '^  ^"*  "'  *^^  ^^'^^^^' 
the  stone  from  a  sL„°  baS.       '*.^"'^'^^««  f^^o™  the  water.    Suspend 

ascertain  itsToss  o^S^^^^^^^  ''  '\^'^  ^"^^  *^-  '"  --'-,  and 

pieces  of  iron,  wood  Tud  other  ,1  .  '  ''f '^'  ^'^^  experiment  with 
it  beneath  a  s^rTace  of  water  ^TT^^'  ^"^'^'^  *  ^^^^'^^'•'  «°d  ^ «rce 
and  it  wi:I  ris^t  tVe  toTof  tlae  ;^^^^^^^^  "^'^^  '^"«-  -"'^  -^^--. 

unLnLThTheTttr"*'  l!  "'"^  ^^  ''  ^^"^^^-^  ^  ^^e  fluid, 

lose  an,  portion  of  their  weight  ZZX:^^  ^^ idf  •^' 

bef^atr^^iU':    wtiVa'lt  IT^^  ^  ^  ^^^^P-  ^^  a  balance- 
ascertain    the^pparent'loss  ofwdA;"    ''  '''' ''^'^  '"  water,  and 

(Fig.  64),  and  weigh  the  beaker  of  water 

with  the  stone  immersed.  How  much  more 

do  the  beaker  and  its  contents  now  weigh 

than  before?    Compare  this  gain  with  the 

apparent  loss  of  weight  of  the  stone  in 

water.    Is  any  weight  really  lost?   Repeat 

the  expadment  with  a  block  of  wood 

Experin.ent  3.    Make  a  saturated  solu- 
tion of  salt  in  water.    Weigh  the  same 
stone  ,n  air,  fresh  water,  and  salt  water 
Compare  its  apparent  loss  of  weight  in 
salt  water  with  that  in  fresh  wnt^r     n 

ence?    Throw  a  piece  of  tor  In  n  ^'''''  ''''''''"'  ^"''  t''^' <li«Vr 

like  cork  on  watef  Fill  a  ve  sel  witrr^  •"  "-^'^  "'*'"' "^^-"•>' 
bubble,  and  drop  it  into  the  ve  1  It  w  11^^  t  T ''  ''"^  '  ^"'^"• 
rolls  over  the  side  and  taultTf]    «  ^'  ""''  '"  *''"  ^'««''^el,  but 

have  greater  ly^^^tVrfX^^^^^  .'*  '''""■'''' ''''  ^^^  «>-'« 

in  Palestine,  is  so  salt  thTA  ^  '  ^''''  "'^*''"  «^  "'«  ^^^ad  Sea, 
the  reason?  ""'  '  ''''''''  ^°««  "°'  ^'"k  in  it.    Can  you  se^ 


Fig.  64. 


fti'il 


!    II 


80 


DY-SAmCfi. 


V\g.65. 


65)  to  .e  .  eubieal  Moo.  of^3f  i^L^^^^^,  ^^  ^^t 
obvious  that  the  downward  pressure  upon 
the  surface  (Za  is  equal  to  the  weight  of  the 
column  of  liquid  edao.     The  upward  pres- 
sure   on    the    surface   cb   is   equal   to  the 
weight  of  a  column  of  liquid  echo.     The  dif- 
ference between  the  upward  pressure  against 
cb  and  the  downward  pressure  on  da,  is  the 
weight  of  a  column  of  liquid  ecbo  less  the 
weight  of  a  column  of  liquid  edao,  which  is 
a  column  of  liquid  dcba  (ecbo  -edao  =  dcba) 
But  a  column  of  liquid  dcba  has  precisely 

ltr!:Zv'  ""  ^^"'  ^"""^'•«^^^-    '^^--^-^'  ^  -''-'^  '-'^  buoyed 
up  by  afluv^      rnnsequence  of  the  unequal  pressures  upon  its  ton 

that  fluid  equal  in  volume 
to  the  solid  immersed.  The 
last  proposition  is  gener- 
ally  stated  as  follows :  A 
solid  loses  in  iveight  as 
much  as  the  tveight  of  the 
fluid  it  disj)laces. 


Flpr.  66. 


Experiment  4.  The  last 
statement  may  be  verified 
with  apFiaratus  like  that 
shown  in  FiKiireCG.  Fill  the 
vessel  A  till  the  liquid  over- 
flows  at  E.  After  the  over- 
flow ceases,  place  a  vessel  c 

under  the  nozzle.     Snspend  m 

a  stone  from  the  balance-b.-an,   R    ...h    r,^^.^.    -,    ■       ■ 

carefully  lower  it  into  the  lion  i     '.  "      '^  '"  "''"'  ""^  tl'^n 

into  the  vessel  c.     Tl.e  ve    e    c  h!  ""  T"  "'  "''  ''''"'*•  ^"'  ^^^ 

vessel  c  having  been  weighed  when  empty, 


'g- 


BUOYANT  FORCE  OF  FLUIDS. 


81 


weigh  it  again  with  its  liquid  contents,  and  it  will  be  found  that  its 
increase  in  weight  is  just  equal  to  the  loss  of  weight  of  the  stone. 

Experiment  5.  Next  suspend  a  block  of  wood  that  will  float  in  the 
liquid,  and  weigh  it  in  air.  Then  float  it  upon  the  liquid,  and  weigh 
the  liquid  displaced  as  before,  and  it  will  be  found  that  the  weight  of 
the  hquid  displaced  is  just  equal  to  the  weight  of  the  block  in  air 


Fiir.  67. 


Hence,  a  floating  mass  displaces  ?is  own  weight  of  liquid ;  in 
other  words,  a  floating  mass  will 
sink  till  it  displaces  an  equal 
weight  of  the  liquid,  or  till  it 
•reaches  a  depth  where  the  buoyant 
force  is  equal  to  its  own  weight. 


Experiment  6.  Next,  partially 
fill  with  water  a  glass  (Fig.  67) 
graduated  in  cubic  centimeters  and 
fractions  of  the  same.  Note  the  level 
of  the  water.  Drop  one  of  the  solids  into  the  water,  and  note  again 
the  level  of  the  water.  The  difi-erence  between  the  two  levels  is  the 
number  of  cubic  centimeters  of  water  that  the  solid  displaces.  But 
one  cubic  centimeter  of  water  weighs  one  gram.  How  does  the  num- 
ber of  cubic  centimeters  of  water  displaced  compare  with  the  number 
of  grams  the  solid  apparently  loses  in  weight? 


vil 


There  is  au  adage  that  "  a  pound  of  feathers  weighs  more 
than  a  pound  of  lead."    Is  there  truth  in  the  statement? 


Experiment  7. 


Fig.  68. 


Instead  of  feathers,  we  will  employ  a  hollow  globe 
a  (Fig.  08) ;  in  place  of  the  "  pound  of  lead,"  we 
will  use  a  counterpoise  6,  of  any  metal  whose 
weight  is  just  equal  to  the  weight  of  tlie  globe. 
Then  when  the  globe  and  counterpoise  are  sus- 
pended from  the  opposite  arms  of  the  balance-beam 
c,  the  beam  will  be  horizontal.  Now  place  the  whole 
on  the  plate  of  an  air-pump,  cover  with  a  receiver, 
and  exliaust  the  air.  What  happens  when  the  air  is 
partially  exhausted?  How  do  you  explain  the 
phenomenon? 


•     '-i'i 


il 


82 


DYNAMICS. 


A  pound  of  feathers  displaces  more  air  than  a  pound  of  lead, 

Dold'ofr^°''L-^".Tf  "P"^°''^^'^^  ^^^'  consequently  the 
pound  of  lead  which  balances  a  pound  of  feathers  in  the  air, 

ZZT^fT"  '^'"^  ^°  "  ""^""'"-     ^«  ^^^r»  ^'^^  the  experil 
menttl,at^od^es^eigh  less  in  air  than  in  a  vacuum,  and  that 

rjiL     '""  ""^'^  '-^^  ''''^'  ^^^^^  "^-  --^^^^  - 


i!^ 


the  sir  ace  of  tt     ^h'*  ?t  ^^^^^^^^  <>f  '^^  atmosphere  is  greatest  at 
whilP Td?  ,  '*'^*'-    ^  •'^^y  ^'•"^  *«  '"^^'^  cannot  remain  at  rest 

lo^n     M  .^  *''f  "^'^  '^""  '''  °^^°  ^«'Sht  of  a  fluid;  therefore  a  bal 

ban  aTrt  th'  '  'T  1''  '"^1  "'*^  ^^'^^  ^^-*  fourt;en  tSighter" 
than  air  at  the  sea-level.  will  rl^e  till  the  balloon,  plus  the  wei^^ht  of  the 

car  and  cargo,  equals  the  weight  of  the  air  displaced.    tL  a    o^^^^^^^^^ 

Wishing  to  ascend  still  higher,  throws  out  a  portion  of  his  cargo  Th 

Soo^n  h?°''  ''  f '"^  ^""^  ""^  ''^  ^'^  '«  --P«  at  th  t'op  orthe" 
balloon  by  means  of  a  valve,  which  he  controls  by  means  of  a  cord 
passing  through  the  balloon  to  the  car.  ^ 


QUESTIONS. 

1.      Why  is  it  difficult  to  stand  in  water  reaching  the  neck? 
lift  whrnoTo";^"  '•'^^^^^  «*«-  -^— '-.  Which  he  cannot 

Pll  wl^nraungr  "^'^'^  '""'  "^^*  "^'^^'  ^'  ^'^  ^^  ^^  dis- 
place? ^'"''  ''''^^'  ""'  ""''""'^  '''"  *  P'"^^  '^^  ^'•°"  weighing  600«  dis- 


VI.     DENSITY  AND   SPECIFIC  GRAVITY. 

§62  Density.  We  speak  of  a  piece  of  cork  as  beinc 
heavier  than  a  nail,  at  the  same  time  that  we  speak  of  cork  al 
l.ght  and  iron  as  heavy.  This  seeming  contradiction  is  ac- 
counted for  by  the  different  meanings  which  we  attanh  to  the 
terms  hgnt  and  heavy.  In  both  cases,  light  and  heavy  are  used 
as  terms  of  comparison.     In  the  former  instance,  we  compare 


iH 


SPECIFIC  GBAVITr.  g3 

the  weights  of  the  two  particular  bodies,  without  reference  to 
vohime  ;  m  the  latter,  we  call  cork  light  and  iron  heavif,  having 
no  particular  bodies  in  view,  but  because  we  know  by  experience 
tha  cork  is  not  so  dense  as  iron,  i.e.,  a  given  volume  of  cork 
contains  less  matter  than  an  equal  volume  of  iron.  The  term 
we^ht  refers  simply  to  the  number  of  grams,  kilograms,  etc., 
that  a  particular  body  weighs,  without  reference  to  the  materia! 
or  the  volume.  The  density  of  a  body  can  be  stated  only  by 
expressing  (or  understanding)  two  quantities,  viz.,  mass  and 
IJTn'   Z^"  '"T;"^'^''  '"PP"""  ^^^'  ^  '^^^^'^  «f  ^«°^^  "^e^^ures 

then      ""«  «  0    '°1  s'o'o'  "^"""if  ^'''•'  ""^^^'^  ^^^' '  '^'  ^^^^^^y  is 
"2^10  X  2u  —  jD?y  =  0.75  gram  per  cubic  centimeter.   When 
we  speak  of  cork  as  lighter  than  iron,  it  is  evident  that  we  are 
comparing  the  densities  of  these  two  substances. 

§  63  Specific  gravity.  TJ^e  specijlc  gravity  of  a  sitbstance 
IS  theratio  of  the  density  of  that  substance  to  the  density  ofanother 
substance  assumed  as  a  standard;  in  other  words,  it  is  "the  ratio 
of  the  weight  of  a  certain  volume  of  that  substance  to  the 
weight  of  the  same  volume  of  another  substance  which  is  taken 
as  a  standard. 

To  facilitate  comparison  of  densities,  uniform  standards  are 
adopted.     Distilled  water  at  its  maximum  densitv,  at  4°  C    is 
the  standard  of  specific  gravity  for  all  solids  and'liquids      In- 
asmuch as  one  cubic  centimeter   of  water  weighs  one  gram 
when  the  weight  of  one  cubic  centimeter  of  any  substance  is  given 
m  grams,  i.e.,   when  its   density  is  given  in  its  usual  metric 
units,    the  same   number  also   expresses  its   specific  gravity. 
Ihus,  one  cubic  centimeter  of  water  weighs  one  gram,  and  1 
IS  the  specific  gravity  of  water.     The  density  of  silver  is  10  53« 
per  cubic  centimeter ;   hence  the  specific   gravity   of  silver  is 
10.53.      The  standard   for  gases  is  air' at   the   average   sea- 
level  density,  and  at  a  temperature  of  0°  C.     The  weigJit  of  one 
cubic  centimeter  of  air,  under  these  conditions,  is  O.^Oo"l2932« 
or  about  ^1^  of  the  weight  of  one  cubic  centimeter  of  water. 
Let  G  =  the  specific  gravity  of  a  substance  ;  D  —  its  densitv 

»  qomu  physiclste  adopt  l.ydrogon  jfas  ««  a  standard  for  gases. 


!i<i;i 


'i' 


84 


DYNA3HICS. 


in  grams  per  cubic  centimeter ;  V  =  the  volume  of  a  given  body 
of  it  in  cubic  centimeters ;  W  =  the  weight  of  the  given  body 
in  grams ;  W  =  the  weight  in  grams  of  an  equal  volume  of  the 
standard.  Then,  as  shown  above,  D  =  ^,  and,  by  definition, 
tr  =  — ,  •     G  is  numerically  equal  to  D,  and  W  to  V. 

Since  the  loss  of  weight  of  a  solid  immersed  in  a  liquid  is 
just  the  weight  of  an  equal  volume  of  that  liquid,  it  is  evident 
that,  if  we  divide  the  weight  of  a  solid  in  air  hy  its  loss  in  weight 
when  immersed  in  water,  the  quotient  will  be  its  specific  gravity. 

Experiment  1.  Obtain  small  lumps  of  glass,  iron,  lead,  marble, 
granite,  etc.,  and  weigh  each  in  air.  Partly  fill  with  water  a  measur- 
ing-beaker graduated  in  cubic  centimeters,  and  note  the  level  of  the 
water.  Drop  a  lump  into  the  water,  and  note  the  level  again.  The 
rise  of  water,  as  indicated  by  the  graduated  scale,  gives  the  volume 
(V)  of  the  specimen.  With  these  data  find  the  density  (D) ,  employing 
the  formula  D  =  — .  Next  weigh  each  of  these  lumps  submerged  in 
water,  and  find  its  loss  in  weight;  and,  from  the  data  obtained,  ascer- 
tain G  from  the  formula  G  =  ^^.  Prepare  blanks,  and  tabulate  your 
results  thus  :  —  "' 


Name  of 
Substance. 


W 

e 


ii'lint  glass. 


435 


V 

ccm 


D 

orG 


134 


3.24 


09— 


W 


water, 


e 8 


W 


435 


305 


130 


G 
orD 


3.34 


.01+ 


Av. 


3.29 


.04- 


SPECIFIC    GRAVITY.  §5 

When  the  result  obtained  differs  from  that  given  in  the  table  of  spe- 
c  flc  gravities  (see  Appendix,  page  402),  the  difference  is  recorded  in 

"'inn  TVk  '"■""■,'  ^'' •  '^*^'"  '^'  '^"^^^ ''  8'"«^*«r  'b*°  the  latter,  it 
is  Indicated  by  a  plus  sign  affixed  to  the  number;  when  less,  by  the 
mmus  sign.  The  results  recorded  In  the  column  of  errors  are  not  nee 
essar  ly  real  errors ;  they  may  indicate  the  degree  of  impurity,  or  some 
peculiar  physical  condition,  of  tlie  specimen  tested. 

Experiment  2.  Obtain  good  specimens  of  cork,  oak,  elm,  and  poplar 
woods,  all  of  which  float  on  water.  Tie  to  a  specimen  a  piece  of  lead 
heavy  enough  to  sink  it;  immerse  the  two,  thus  attached,  in  a  measur- 
ng-giass,  and  find  the  number  of  cubic  centimeters  of  water  displaced  by 
them.  In  the  same  way  find  the  amount  displaced  by  the  lead  alone. 
Subtract  the  amount  displaced  by  the  lead  from  the  amount  displaced  by 
tlie  two,  and  the  remainder  will  be  the  amount  displaced  by  the  specimen. 
Then,  regarding  the  number  of  centimeters  of  water  displaced  as  so 
many  grams,  apply  the  formula  G  =  ~ . 

W 
Example.  Find  the  specific  gravity  of  a  piece  of  elm  wood.    At- 
tach to  It  a  piece  of  lead  weighing  (say)  408. 

The  combined  solids  displace 28.6«  of  water 

The  lead  displaces 3  gg        „ 

The  elm  displaces ^^        „ 

The  elm  weighs  in  air [   20.08         " 

The  specific  gravity  of  elm  wood  is  .     .    !   20.0-^ 25=. 8. 

Experiment  3.  Find  the  specific  gravity  of  alcohol,  a  saturated  so- 
lution  of  common  salt,  sea-water,  naphtha,  olive-oil,  pure  milk,  and 
mercury  in  the  follow  :,  manner:  ascertain  the  loss  in  weight  of  a 
sinker  in  each^one  of  these  liquids,  also  in  water,  and  then  apply  the 
formula  G  =  — .  Here  W  «nd  W  represent  the  loss  of  weight  of  the 
sinker  in  the  liquid  and  water  respectively. 

Example.  Compute  the  specific  gravity  of  alcohol  from  the  foUow- 
mgdata:  — 

A  piece  of  marble  weighs  in  air     ....  66.808 

The  same  weighs  in  water 36.808 

Loss  in  water 2o!oob 

_,  56.808 

The  marble  weighs  in  alcohol 40.968 

Loss  in  alcohol j^ 


il! 


^1 


86 


DYNAMICS. 


Since  20K  and  15.84*  are  the  weights  respectively  of  equal  volumes  of 
water  and  alcohol,  and  since  G=^,,then  -^^=Jd2.  the  specific 
gravity  of  alcohol. 


FIk.  (;<!. 


§  64.  Hydrometers.  —  Experiment.  Take  a  unif f)rin  rod  of 
light  wood  about  a  foot  long,  and  mark  off  on  it  a  scale  of  eciual  i)arts. 
A  convenient  size  is.  »  inch  square,  and  a  suitable  scale  is 
Inches  and  half  inches.  Coat  the  rod  with  parattine  to  pre- 
rent  its  absorbing  water  and  swelling.  Bore  into  the  end 
marked  zero  a  hole  about  2  inches  deep,  and  drive  in  bullets 
till  the  rod  will  sink  in  water  (Fig.  69)  just  to  some  inch- 
mark,  and  stop  the  end  with  parafflne.  If  it  sinks  too  deep, 
cut  off  the  upper  end  of  the  rod. 

Suppose  the  rod  sinks  8  inches  in  water;  then,  if  it  is  |  inch 
square,  it  displaces  2  cu.  in.  of  water.  The  weight  of  the 
water  displaced  must  just  equal  the  weight  of  the  rod  (see 
§61J.  Now  immerse  it  in  alcoliol;  it  sinks  deeper,  say  to 
the  10-inch  mark;  that  is,  Y  cu.  iu.  of  alcohol  weigh  the  same 

V      8 


as  f  cu.  in.  of  water;  therefore,  G  =  -^=— =  .800.    If  in 
brine  it  smks  only  C|  in.,  G  =  —  =  1.20. 


10 


"J 


Apparatus  like  that  described  is  called  a  hydrometer.  In- 
stead of  a  rod  of  wood,  a  glass  tube  is  generally  used,  ter- 
minating in  a  bulb  containing  shot  or  mercury.  Tlie  tube  _  _^ 
contains  a  scale  with  numbers  corresponding,  which  express  the  specific 
gravity,  so  that  no  computation  is  necessary.  Make  solutions  of 
various  substances,  and  test  their  specific  gravity  with  your  hydrome- 
ter, and  test  the  accuracy  of  the  results  so  obtained  by  other  processes. 

The  most  direct  way  of  finding  the  specific  gravity  of  liquids 
and  gases  is  by  employing  vessels  that  hold  definitJ  weights  of 
the  two  standards,  water  or  air,  and  then  weighing  these  vessels 
when  filled  with  other  liquids  or  gases ;  .ind,  after  deducting  the 

weight  of  the  vessel,  applying  the  formula,  G  =  —  • 

W 
The  specific  gravity  of  a  solid  that  is  dissolved  by  water  may 
be  found  by  weighing  it  in  a  liquid  that  will  not  dissolve  it 
(e.g.,  rock-salt  in   naphtha);   and,  having   found  its  specific 


lIYnUoMHTKUa. 


ft7 


gravity  as  compared  witli  the  liquid  used,  multiply  this  result  by 
tile  specific  gravity  of  tlie  liquid. 

From  the  formula  D  =  :| ,  we  have  V  =  | ;  hence,  the  volume 

of  an  irregnlar-shaped  body  may  he  found  in  cubic  centimeters  by 
diouhng  Us  neight  in  grams  by  its  density. 

Again,  from  the  formula D  =  ^,  we  have  W=Vx  D.  Hence. 

tvhen  the  volume  and  density  of  a  body  are  knotvn,  its  weight  in 
grams  may  be  found  by  multiplying  its  volume  in  cubic  centime- 
ters by  its  density. 


! 


QUESTIONS  AND   PROBLEMS.' 

1.  How  high  can  sulphuric  acid  be  raised  by  a  lifting-pump? 

2.  VVhat  IS  tlie  weiglit  of  508  of  water  in  water? 

8.  Find  the  specific  gravity  of  wax  from  the  following  data :  weight 
of  a  given  mass  of  wax  in  air  is  80^;  wax  and  sinker  displace  102  88ccm 
ot  water;  sniker  alone  displaces  14'^='". 

4  Why  does  a  light  liquid  Ce.g.,  oil),  introduced  under  a  heavier 
liquid  (e.g.,  water),  rise?  •        "«*^'*-'^ 

6.  Glass  is  about  three  times  heavie-  .  water-  how  then  can  « 
glass  tumbler  float  in  water?  '         '    *° " 

6.  How  can  iron  vessels  float  in  water? 

7.  A  block  of  ice  containing  oOOecm  is  floathig  on  water;  how  many 
cubic  centimeters  are  out  of  water?  "vv  luauy 

8.  Will  ice  float  or  sink  in  alcohol? 

9.  How  much  more  matter  is  there  in  500<=em  of  sea-water  than  in 
the  same  volume  of  fresh  water? 

10.  In  50k  of  gold  how  many  cubic  centimeters? 

11.  What  is  the  density  of  gold? 

12.  What  is  the  density  of  cork? 

ture'of To'cV'  '''"  '"'"'"'^  "'  "''  ^*  "^''""'^  P''^^^^'-^'  *"^  ^'  *  t«™P«ra- 

14.   An  Irregular  piece  of  marble  loses  53«  when  weighed  in  water 
How  many  cubic  centimeters  does  it  contain  ? 
16.   When  will  a  body  sink,  and  when  float? 

iAj  «.,!^fi  „,,  muuu  as  !•""  of  water? 

>  Consult  the  Tables  of  Specific  Gravities.  In  the  Appendix.  Section  O. 


ii:u 


M 


ill 


88 


DYNAMICS. 


17. 

is. 

19. 
SO. 
21. 


How  much  will  Ik  of  copper  weigh  in  water? 

What  does  a  piece  of  load  20  x  10  x  5cm  weigh? 

What  will  it  weigh  in  water? 

What  will  it  weigh  in  mercury? 

What  becomes  of  the  woiglit  that  is  lost? 
..1       " i^lu^ f "  ^"^  dissolved  in  Ii  of  water,  without  increasiuff  the 
^^olume  of  the  liquid,  what  wi,l  be  the  specific  gravity  of Ihe^som! 

vacu'umi  """''  ''  ''""  """^^^  '"  '°  ^''-    ^^'^^  ^"'  '^  ^^'^S^  in  a 

24.  A  mass  whoseVvelght  in  air  is  308,  weighs  in  water  26«  anrt  <n 

another   liquid    m     What   is    the   specific 'gravit?  of  «r"othlr 

26.  A  silver  spoon,  weighing  1508,  is  supported  by  a  string  in  water 

s:^^:rb;tt  ::;s;  '^  --^-^  ^^- «---  -L;rtt 

S"  tr  Ta^'fT'""  ''^""  ^'  '''''''■    "''^  "'"^'^  ^-««  it  weigh? 
It  displace?  '""""  ^''''^  *°  *'^  ""'"'^  '''^  ^^'^  watef  would 

28.  If  the  boat  is  capable  of  displacing  lOO'bm  of  water  whnf  w^i^hf 
must  be  placed  in  it  to  sini<  it?      *^        °     "      oi  water,  what  weight 

29.  An  empty /:;lass  globe  weighs  lOOR;  full  of  air  it  weighs  102  4k- 

S'ktrgiv""' '' '''''''  '''■''''■  ""'^^  *«  ^^«  speciflri^v:; 

^^  ?0.  What  weight  of  alcohol  can  be  put  iuto  a  vessel  whoso  capacity 

31.  You  wish  to  measure  out  50?  of  sulphuric  acid.    To  what  num 
hereon  a  beaker   graduated    in    cubic  centimeters  wUl  ttt  coJr" 

Ing'beater  ''°''  ^°"  """"'^  ""'''"'"'  """^  ^^'  "^  "*''''^  "^'"^  '="  ^  '"^««"'- 

weight  VtretptS'"  "°*^'"^  ''''^  ^^  ""'^""•^-     ^~  »«  *»- 

vn.?"  wi^'"!'''^^  ''  ''''"^''^  ^^"^  ''"^''^  *h«  ^"''f'ice  of  water  in  a  reser- 
sulZlT  '""*'"--^°^'^«  P-«^--  ->''-ter  must  it  be  capable  of 

85.  A  cubical  vessel,  each  of  whose  sides  contains  2500nem  ig  fl,|„j 

6  T:  „7r  f """"  '^^^^  '''  ^'""'^"^  «-*'""^    0"->^  it«  nicies' 
»>,,!;,       ?       ^^  ^  ''*  *  '''^''**'"  '"'■P"'  '"  '^  "yuid  when  the  vessel 
which  contains  it  is  in  the  air;  If  the  vessel  is  placed  in  .  v«.nn  J  1^ 
tne  solia  siuk,  riae,  or  remain  stationary?  """  '  " 


MOTION. 


89 


;!i 


VII.    MOTION. 

;n  *e  o«.  ever,  j„,:;;ir  t:? ::~:  r:;^^^^ 

Ins  attent  on  to  obiects  hv  tha  «,„     -^  '       '  ^^*^  '"'"  f^»ect 

"-t  »„  i„  t,.e  ea7a«  i'' S' t'aU  '  ""  °T  "'  '"'«°-- 
i-eferecee  to  certain  object^  a  Ji„     T"  ""^  ""^  "'  «'^'  "'«' 

object  eonsidered  apart  '  ^arotC  "1^  """"""""^  "^  "■' 
object  except  with  refcre,.  ^Z[  .!  .  "•■"""""  '<"="«<=  «n 
ceive  o,  eJnge  or'  ^Z:^^^^^':,'  ""v""  ^"  «"'• 
i»  relation  to  some  other  object     £  "'''"•''  "«"?' 

rate  of  sixty  miles  an  ho„t  knows^M  tlLTT  '  "°""^  ■•"  '"« 
till  he  looks  away  from  hi,  baZn       ]  "  """'"«  "'  "". 

passing  in  panotla  10"^  ""^  ""'^  "■"•  '"""^ 

§66.  All  matter  is  in  motion       77,.      . 
absolute  rest  in  the  universe.   There  i«Tn!  "  T  "^'^  ''"'^^^  «^ 
cept  t.  indicate,  with  -fereLe  ^l":,':;  ^^  t^^^r '  - 
objects  that  are  movin-  in  tho  «„         ,         '  ^''^  ^'O^dition  of 
same  velocity.     For  e ":«!   .  j'"""'"""  «"^  ^'"'  ^he 

riage,  at  the  L  of  te"  mTel  au  hoT  """  '""'"^  ^  -- 
to  each  other  and  the  ^  ria  "  T,'  T  "'''  ^^"^  ^^^^''^^^^ 
only  be  .sed  in  an  ex  r  mefv  ii  J  ,  '  "''^"  "  ^'  ^^«' "  «-« 
language  refers  only  to  t  e  ec^^^j  ^^^^  ^^"r'  '"'  ''  ^^'"'"^^ 
to  that  on  ^vhich  it  stand  as  .  J  T  ^^■"'*  "'"•'''  ••^^f^'-«"^« 
of  the  earth.     It  isZtCLT      ''  "'  "^  ^''''''  ^'^  -"'f'-- 

'notions  of  the  eanhtULCiror^'  7'  ^^  '^'"^'  ^'^^ 
as  being  at  rest.  '   ^  ""^  ""^^  terrestrial  object 

chf^;i:L:x;:::r^^^   - « who,e,  or  visile  „.. 

then.ss,-an^n;ir:je:r:„r\rr-^ 
-not  «ee  the  movements  of  the  mole^Ie^  ^^"irbut  Zl 


m 


m 


«h: 


III 

m 


tl 


90 


DYNAMICS. 


know  that  they  exist  by  their  great  power,  manifested  in  moving 
machinery. 

§  67.    Velocity.  —  Uniform  and  varied  motion. —  All 
motion  taltes  time ;  hence  the  term  velocity,  which  refers  to  the 
space  traversed  in  a  unit  of  time.     Motion  may  be  uniform  or 
varied :  uniform,  when  an  object  traverses  successively  equal 
si)aces  in  aJl  equal  intervals  of  time;   varied,  when   unequal 
spaces  are  traversed  in  any  equal  intervals  of  time.     Varied 
motion  may  be  accelerated  or  retarded :  accelerated,  when  the 
paces  traversed  increase  at  each  successive  interval  of  time ; 
retarded,  when  they  diminish.     The  motion  of  a  train  of  cars,  in 
Btarting  from  a  station  is  at  first  accelerated,  afterwards  tolerably 
uniform,  and  when  the  braked  are  applied,  it  becomes  retarded. 
Strictly  speaking,  all  motions  are  varied  ;  there  is  no  illustration  of 
absolutely  uniform  motion  in  Nature  nor  in  art,  though  we  may 
conceive  of  its  possibility  and  have  very  closely  approximated  to  it. 

The  velocity  of  a  body  having  accelerated  or  retarded  motion  can 
l)e  given  only  at  some  definite  point  l)y  an  estimate  of  the  distance  it 
would  traverse  in  a  unit  of  time,  were  it  to  continue  in  uniform  motion 
at  the  speed  it  lias  at  that  point.  For  instance,  a  railway  train  passes 
us,  and  we  estimate  that  its  velocity  is  30  miles  an  hour,  although  in  a 
few  minutes  its  speed  may  be  reduced  to  10  miles  an  hour,  and  a  little 
later  it  may  come  to  rest.  When  we  assign  a  velocity  of  30  miles  an 
liour,  we  have  no  thought  of  whether  it  will  run  30  miles  during  the 
next  hour,  or  whether  it  will  riui  an  hour;  we  mean  that,  should  it 
retain  its  present  speed,  it  wiU  be  30  miles  away  from  us  at  the  end  of  au 
hour. 


VIII.  FIRST  LAW  OF  MOTION.  —  INERTIA. 
Now,  what  is  it  that  sets  in  motion  that  which  was  previously 
at  rest?  We  may  call  it  force;  but  what  idea  does  this  terra 
convey?  Let  us  question  our  own  experience.  We  leave  an 
apple  lying  upon  a  table  ;  have  we  not  entire  confidence  that  it 
will  continue  to  lie  there,  unless  disturbed  by  some  otlier  body? 
If  on  returning  we  find  it  gone,  are  we  not  sure  tliat  it  has  been 
removed  by  the  action  of  some  body  other  than  itself?    An 


riEST  LAW  OF  MOTION.  91 

apple  falls  to  the  ground,  and  although  the  action  is  one  of  the 
most  mysterious  m  all  nature,  yet  do  we  not  almost  instincUvl 

1  he  ball  at  rest  ,s  put  m  motion  by  a  bat ;  but  must  not  the  b.t 

Again,  the  bat,  having  received  motion,  is  capable  of  immrt 
■ng  motion  ,„  the  ball ,  but,  having  sot  in  motion  one  ba™  s 
equally  capable  of  putting  in  motion  another  ball  ?    C«  "  mis 
impart  motiou  and  retain  all  its  motion?    Is  it  not  lit.  „ 
meroial  transaction,  a  trade,  to  which  thcr    ai^  tw    parties"™' 
a  buyer  and  the  other  a  seller?  that  is,  arc  not  all  tCsaeU^ns 

tine  of  a  transfer,  which  should  ho  entered  on  the  debitside  of 
one  s  account,  and  the  credit  side  of  the  other's?  Tj^l 
(2)  that  «„(,o,.  ,„  „„e  bo,hj  is  cause)  only  by  another  boWs 
imrundwill,  so^  of,tspo,oer  of  producing  LL  " 

it  a  sled,  on  which  a  child  is  sitting,  is  siiddenlv  ni.t  i„  „,„ 
.on  the  child  is  left  in  the  place  from  wliie,  "sled  srt"d 
If  theoiUd  and  sled  are  both  in  motion,  and  the  edtsid' 
deny  stop,«l,  the  child  lands  some  distance  ahead  ft 
sled  IS  started  slow^,  the  child  partakes  of  the  niotbu  o 
sed,  and  is  earned  along  with  it;  and  if  the  sled  „rad  ,.,llv 
stops,  the  child's  motion  is  gradually  checked,  and  i  it  "^ 
place  on  the  sled.  This  shows  (3)  that  .^ass^s  of  mXrZZ 
rmtmi  graduuUy  and  surrender  it  gnuluall,,. 

p„,!ti.,„        ton ,  t„h       ?  ,         i|"art2.,a,i,l  is  placccl  l„  a„  olova.,.,l 
melteawax.    When  ceo,,  u.„Ues^„  IsV^'cllT^irrsl^J-X;' 


I.  )i 


m 


92 


DYNAMICS. 


l"rf  ZeS*'  The  nlT;  T"^*''  ''"''  ^"^^^^^  «°'^  -^^^^e  the  lines 
are  traced.    The  plate  is  then  placed  beneath  the  orifice  of  the  tnho 

and  exposed  to  a  shower  of  sand.  The  velocity  of  the  sand-grains  s 
not  at  Its  maximum  at  the  start,  but  is  constantly  accelerated  tiUthl 
reach  the  plate,  where  their  velocity  in  turn  is^radua't  given  up"^ 
The  wax,  on  account  of  its  yielding  nature,  gradually  bXftheVtn 
Tuii  at  it  "  t"'  -*-^«-*-^-g  its  harLss,  cLnrip  t^^ 
quite  at  its  surface;  and,  therefore,  it  suffers  a  chipping  act  on  from 
he  sand.  Thus  the  soft  wax  affords  a  protection  from  the  acHono' 
the  alhng  sand  of  all  parts  except  those  intended  to  be  cut  As tm 
Ttul     Fo:^?""'"^^r"  *^  *^«  ^^'^^  "^y  «*-™  blown  thtough 

metals  like  1!^'  ''''""  '''  ^^P"'"'"^  ''  ^*"«^  *  «««'^-*'«*^-  Hard 
metals  like  steel  are  engraved  in  the  same  manner.    Yet  the  hanrt 

may  be  held  in  the  blast  several  seconds  without  injury.  (What  is  the 
difference  in  the  effects  of  catching  a  base-ball  with  hands  held  rgidlv 
trballPX  '  '''  '''''  '"  '"''  ^'^"^"'^^  '^  the  moS  Of 

m^^.  'I.y^^'.^''  I  ^^^P^*'  -  '*  «o«°  «tops ;  roll  it  on  a  smooth 
maible  floor  _,  rolls  much  farther.    On  a  perfectly  smooth  sur- 
face it  might  roll  for  hours.    If  we  could  provide  such  a  surface 
and  dispense  with  the  resistance  of  the  air,  how  long  would  il 
roll      These  conditions  are  impracticable?    True.     But  have 
not  the  heavenly  bodies  rolled  for  millions  of  years  through  fric- 
tionless  space,  unchecked  because  unimpeded  ? 
strST-  ""°^^;r^*^^  *«  I'^'-Petual.    Motion  undisturbed  is  in  a 
strSt  ,  "^'""^.^^"^^  ^»l  ^  ^-^-ble  roll  more  nearly  in  a 

straight  line,  a  smooth  or  a  rough  floor?     What  if  the  floor  were 
perfectly  smooth?  • 

The  relations  between  matter  and  force  arc  admirably  and 
oTZZr^'''''''^  '"  '"^'''^  '''  ^"""^^  '"'  ^'''''''''  Three  Laa,^ 
rel  ^ndat^^^  ""^  Motion.-^  body  at  rest  remains  at 

That  nnrtnf  tho  l""' ivh!/-v. *-• 

t\.^  r„    .r. "  "  P^'Kiins  to  motion  is  brietlv  8nmmari7PH  In 

the  r.«ar  e.pr.,*.,  ••  pe.pu„„,  „„„„,,.  ..  ^  p^p^fj^^  po'^. 


re  the  lines 
f  the  tube, 
icl-grains  is 
ed  till  they 

given  up, 
gs  them  to 
stop  them 
ction  from 
}  action  of 
It.  A  still 
'n  through 
ast.    Hard 

the  hand 
/^hat  is  the 
2ld  rigidly 
motion  of 

a  smooth 
ooth  811  r- 
.  surface, 
would  it 
Jut  have 
ugh  frie- 

hI  is  in  a 
irly  in  a 
3or  were 

biy  and 

ee  Laws 


\ains  at 

ty  in  a 

change 

irized  in 
ion  pos- 


SECOND  LAW  Ot  MOTIOK 


QQ 

pos^bie  „««^,  ,;,„;*;^  .^znrir'r^--^-'  »<'■-  «•- 

to  do  who  mm  establish  oem.,,..!      ".'"'""•■>■    What  has  a  ncrson 

"'«  it  is  in  with  rXnce  to  1,       "'  *"  '^'»"'»  '"  ""=  ««e 
called  ».«„.    Eviden  iXC'::. hT  '""  '"'^  """""'^  '^ 

«o'-  ia  o,to.  app.,.^toCu:drL  ^"LS  ^"^  - 

^t^ek  by  a  bat  he  wolt^Kr  V"  "■"  """o"  "'  -  "all 
.  (  ;  m  wlut  direction  It  moved,  and  (3)  Ac,™ 

at  I  »d  D%r'"o';  rr^'i' 

hu  hof  J  **  ^  "®  struck 
tively  to  B  and  E  in  one  second  V.  h"""  *'^  """^  ''^P"^"" 
their  starting-points  ;  tlXs  AB?nd  nP  "^''^  ^  ""O  »  "■•'' 
tion  of  their  motions,  and  he  lifts  „f«  ,"""*"'  ""'  "''■"c. 
the  distances  traversU  and  th!    ? ,  '  ''"'="  '"P^''""'  both 

"pplied.     In  readtagthe  dirtct        r  "*"^'*'  <>'  «»  'oroes 
order  of  the  Iet,^:t  A  B t^d  d E  '  '"  '""'"'"«'  "^  "■« 

-=4TtrBtrsrd^--p- 

let  a  force  of  tb„  i,.t„„."" 7'?°"<' '  "'"'-  "t  the  end  of  the  seeo„d 

tion  Of  the  former 'Cattlir^trd""^'-  "  T  *'•- 

second, —  It  would  move 


--      *•>  ""never,  wn 

forces  should  be  applied  at  the 


however,  when  the  ball 


I'- vi 


m 
I 


.Ni 


»sat  A,io^/<ofthe8e 


uame  time,  then  at  the  end  of 


a 


94 


t)YNAMICS. 


%r 


Its  path  will  not  be  A  B  nor 

Fig.  71. 


second  the  ball  will  be  found  at  C. 
AD,  but  an  intermediate  one, 
AC.  Still,  each  force  produces  in 
effect  its  own  separate  result, 
for  neither  alone  would  carry  it  to 
C,  but  both  are  required.  Hence, 
the 


§  69.  Second  law  of  motion. 

—  A  given  force  has  the  same  effect 

in  producing  motion,  lohether  the 

body  on  which  it  acts  is  in  motion  or  at  rest;  ivhether  it  is  acted 

upon  by  that  force  alone,  or  by  others  at  the  same  time. 

§  70.   Composition  of  forces.  —  It  is  evident  that  a  sino-le 
force,  applied  in  the  direction  AC  (Fig.  71),  might  produce  tlie 
same  result  that  is  produced  by  the  two  forces  AB  and  AD. 
Such  a  force  is  called  a  resultant.     A  resultant  is  a  single  force, 
that  may  be  substituted  for  two  or  more  forces,  and  produce  the 
same  result  that  the  combined  forces  produce.    The  several  forces 
that  contribute  to  produce  the  resultant  are  called  its  components 
When  the  components  are  given,  and  the  resultant  required,  the 
problem  is  called  composition  of  forces.     The  resultant  of  tivo 
forces  acting  at  an  angle  to  each  other  is  always  a  diagonal  of  a 
parallelogram,  of  ichich  the  components  form  two  adjacent  sides. 
Thus,  the  lines  AD  and  A B  represent  respectively  the  direction 
and  relative  intensity  of  each  component,  and  AC  represents 
tlie  direction  and  intensity  of  the  resultant. 

Tlie  numerical  value  of  the  resultant  may  be  found  by  com- 
paring the  length  of  the  line  AC  with  the  length  of  either  AB 
or  AD,  whose  numerical  values  are  known.  Thus,  AC  is  2.23 
times  AD;  hence,  the  numerical  value  of  the  resultant  AC  is 
4x2.23  =  8.92. 

When  the  components  art  at  right  angles  to  each  other,  as  in 
Figure  71,  the  resultant  divides  the  parallelogram  into  two  equal 
right-angled  triangles ;  and  the  intensity  of  the  resultant  may  be 


c 
ti 


ce 
on 
inl 


be  AB  nor 


it  is  acted 

it  a  single 
reduce  the 

and  AD. 
igle  force, 
rocluce  the 
sral  forces 
mponents. 
[uired,  the 
nt  of  tioo 
onal  of  a 
zent  sides. 

direction 
epresents 

by  coni- 
ither  A  B 
C  is  2.23 
nt  A  C  is 

ler,  as  in 
wo  equal 
t  may  be 


BESOLUTION  OF  FORCES.  95 

i«und  by  calculating  the  hyi.otiienuse,  havin-^  two  s^des  of  .M^ 
triangle  given.    Thus,  V  l^X^^- «  n,    '"« '^«  ^.d^s  of  eitlier 
the  result-xut  A  C     \\T       J    ."       "^'^''^'"""'-''■'^'''^'^^^"eof 
cicsultaut  A  C.     A\hc-n  the  two  components  of  a  force   F 

lin«  J     .  ^    ^""^  '"  ''  d^-ection  at  riglitan-Ies  to  its 

hne  of  action,  it  is  evident  that  the  resolced  part  of  -t  for^^ 
any    irection  has  tiie  total  oifect  of  that  forced  tl^t '  i       L  ' 

A  B    '  "7V"'^""'  "^'  '"'  *"^  ^-^'^"^^-^^  «f  the  coinpo^n  s 
A  B  and  A  C,  ,M  each  of  the  four  dingnun.  in  Fig.  72      Also 

Fig.  72. 


if, 


assign  appropriate  luunericul  values  to  each  cou.ponent  and  find 
the  corresponding  numerical  value  of  each  resultant!  ' 

yVhen  more  than  two  components  are  aioen   ii»r1  ih. 

.  ™.v  t.o  of,,.,.,  ,„  of,,,.  m,,«„:/;:r:^:t  ::r: : 

tM  evenj  oo,npoue,U  ,ms  l,,en  used.     Thus,  in  Fig    7^/0°" 
Fig- 73.  tlie  resultant  of  A  B  and  A  D, 

and  A  F  is  tlie  resultant  of  A  C 
and  A  E,  i.e.,  of  the  three  forces 
A  B,  A  D,  and  A  E.     (Invent 
several  problems  similar  to  this, 
in   whicli   three,  four,  or  moie 
forces  are  to  he  combined,  and 
work  out  the  results.) 
S71.  Resolution  of  Forces 
certain  distance  in  a  eertai,.  .,i,.~tio,::TcT;;;  rT)"  ^^^  ! 
oueoftho  foree,  a.at  produce,  ..us 'n,„tio     ir.J,  i;™"!    il 
.uten»,tj,  and  direction,  by  the  lino  A  B;  what  mus    b    ', 


lif  ! 


96 


DYNAMICS. 


Ma' 


intensity  and  direction  of  the  other  force  ?  Since  A  C  represents 
in  intensity  and  direction  the  resultant  of  two  forces  acting  at  an 
angle  to  each  other  (§  70), 
it  is  the  diagonal  of  a  paral- 
lelogram of  which  A  B  is  one 
of  the  sides.  From  C,  draw 
C  D  parallel  and  equal  to 
.  B  A,  and  complete  the  par- 
allelogram    by    connecting 

the  points  B  and  C,  and  A  and  D.     Then,  according  to  the  prin- 
ciple of  composition  of  forces,  A  D  represents  the  intensity  and 
direction  of  the  force  which,  combined  with  the  force  A  B,  would 
move  the  ball  from  A  to  C.  '  The  component  A  B  being  given 
no  other  single  force  than  A  D  will  satisfy  the  question 

Had  the  question  been.  What  forces  can  produce  the  motion 
AC-  an  infinite  number  of  answers  might  be  given.  In  a  like 
manner,  if  the  question  were.  What  numbers  added  together 
will  produce  50?  the  answer  might  be  20-f-30,  40-f  10  20-1- 
20-f.lO,  and  so  on,  ad  infinitum;  but  if  the  question' were 
What  number  added  to  30  will  produce  50?  only  one  answer 
could  be  given. 

Experiment.    Verify  the  preceding  propositions  in  the  following 
manner:  From  pegs  A  and  B  ^ujio^ing 

(Fig.  75),  in  the  frame  of  a ^''^-  '•'• 

blaclcboard,  suspend  a  Itnown 
weight  W,  (say)  10  pounds,  by 
means  of  two  strings  con- 
nected at  C.  In  each  of  tliese 
strings  insert  dynamometers' 
X  and  y.  Trace  upon  the  blaclc- 
board  sliort  lines  along  the 
strings  from  the  point  C,  to 
iniUcate  the  direction  of  the 

two  component  forces;    also  _^^^^^^^^ 

trace  the  line  CD,  in  continuation  of  the  line  WC   t     •  ^-  , 


given, 


RESOLVED  PARTS  OF  FORCES. 


97 

be  found  that  10  .-  „un,ber  of  pomK,     ''T"  *'  *  ^'«^"'^«'-     ^^  ^i" 
-  :  C  D :  Ca ;  also  that  10    nlbe    of  "l  T'  r"  ""  ^y-mometer 

I'ounds  must  act  i„  the  direction  C  D  to  n  \"  ^^'  ^  ''"^'^^  ^«»'^«  «f  ^0 
l>'-"<'»ced  hy  the  two  compone"  s  IW  '"T'  '''  ■'^'^™^  ^*^«"^*  ^^at  is 
^ra.n  represent  tke  intJuyTn^  dU^UoZ/:  '"""''"  ''•^«^-«^'^"'- 
'^'"^"""^  re^r..e«^.  ^/.a  resultant  Y'vyZ  {  m  '^"'"^'"'"'^  Z"^^".  ^A. 
strings  fron.  different  points,  as  E  and  p  A  aSl!'!  "^  '"'^'"'^"^'  "''^ 

§  716.    Finding  the  Resolved  Parts  of  Porno.       r, 
SHke  of  bievitv  we  will  ..^l!  .  f  Forces.  -For  the 

the  length  of  i  C  Ind  "■"''^""'•^'"^  ^"  '"^^"-'y  by 


FiG.A. 


in    direction    by   the 

direction  of  A  C,  the 

force  A  C.     Let  D  B 

^e  a  rectangle  (Fig. 

A).     From  what  has 

been  said  (page  95), 

it  will  appear  that  the 

forces  A  B  and  A  D 

are  the  resolved  D-ii-fQ  r^t  *u     .. 

«   an.   A  D,  re^^/ely^^^  'Z\^ l^  '''  ''^^^  «^  A 

-"gle  C  A  B  is  given,  A  B  and  A  D  t  ^'^'"'  ""^  '^^ 

ever,  as  we  wish  to  d^al  onlv  I'tt       '"'^  ^'  ^^""^-     ««^- 

nmtics,  we  shall  consider  onlv  thll    ^^'^  .^^e^^entary   mathe- 

C  A  B  is  30%  4.5°,  or  60°.      ^  '^'''  '"  ^^'^^  the  angle 

If  the  angle  CAB  is  "in"    fi      c  • 

A  C,  and.  flw.i.-.f....„    *   T.        \/>  2 


A  C,  and,  thei-efore  A  1}  =  ^l 
angle  C  A  B  is  45°,  A  B 


AC  (Euclid  I.,  47).     If  the 


therefore  A  B 


'8  60°,  the  angle  A  C  B 


-J  A  B  =  BC  (Euclid  I.,  32  and  6), 

2-AC(EuclidI.,47).     If 


and 


the  angle  CAB 


IS 


md  therefore    -  B  is  ^  A  C. 


1 
I 


m 


im 


fi 


98 


DYNAMICS. 


From  the  above,  of  the  truth  of  which  the  student  shoukl 
thoroughly  satisfy  himself,  it  will  be  seen  that,  the  resolved  pa^t 
of  a  force  Fin  a  direction  makiny  an  an>jh  of  6'(f  ivith  its  line 
of  action  is  F  x-^;    if  the  angle  is  45°  the  resolved  part   is 

^  X  -  "2  '  -^  ^''^  ""^^^^  '^  <^^°'  '''«  resolved  part  isF  x  i;  and  if 
the  angle  is  .90°,  the  resolved  part  is  zero.  These  fo.ir  fuels 
should  be  carefully  remembered  as  they  will  be  found  exceed- 
ingly useful. 

QUESTIONS. 
l^n^■h  ^'""i  the  vertical  and  horizontal  resolved  parts  of  a  force  of 
100  lbs    whose  Ime  of  action  makes  an  angle  of  .JQO  with  the  vertical 

2  A  picture  weighs  20  lbs.,  and  the  two  parts  of  the  suspM.sion- 
cord  make  with  each  otiier  at  the  nail  an  angle  of  GO"-  whitisX 
tension  of  the  chord?  '       *''*  '**  *''*' 

3.  If  a  body  is  in  contact  with  a  smooth  surface,  why  is  the 
pressure  between  the  body  and  surface  nt  ri.kt  an, l.  to  thesnrfa     ? 

4     Why  ,s  the  pressure  between  a  fluid  and  a  surface  in  contac 
with  It  at  right  angles  to  the  surface? 

5.  Why  can  a  sailing  yacht  make  progress  in  a  direction  at  ri-hf 
angles  to  the  direction  in  which  the  wind  is  blowing?  m  v^hrpos mon 
must  its  sail  be  set?  position 

6.  What  is  tiie  force  which  raises  a  kite? 


FiG.B. 


if! 


resolved 


Composition  of  Forces 
by  First  Finding  Resolved 
Parts.  -  Let  two  foices  of 
H  lbs.  and  \0  lbs,  act  along 
the  lines  A  B  and  A  C  (Fig° 
B),  and  let  the  angle  BAG 
=  60°.  Find  the  resultant 
of  these  two  forces. 

For  the  force  of  10  lbs., 

substitute  its  resolved  parts 

along  A  B  and  A  H. 

angle  C_A  H  =30°,  these 

ind  5  VS  lbs.  along  A  II. 


COMPOSITION  OF  FORCES. 


ent  should 
■.solved  part 
t'th  Us  line 

Jed  part   is 

:  h  ;  ami  if 

four  facts 
id  exceod- 


a  force  of 
J  vortical. 
siKsp.'ii.sion- 
vvliiit  is  tlie 

liy    is    the 

lie  surface? 

in  contact 

on  at  right 
at  position 


if  Forces 
Jesolved 

forces  of 
act  along 
V  C  (Fig. 
:Ie  BAG 
resultant 

■  10  lbs., 

'ed  parts 

[. 

0°,  these 

ig  A  II. 


Draw  A  H, 
making  the  angle 
Ji  A  II  =  30°, 
and  draw  N  A  K 
at  right  angles  to 
AH. 

Now  it  is  easi- 
ly seen  that  — 
tlie  anglos 

B  A  N  =  (J0°  ; 

C  A  N  =  4r>° ; 

C  A  K  =  4r>°. 

For  the  force 
of  6  lbs.,  acting 
along  A  B,  sub° 
s.it,,.e^i.   „so,voc,  part«,  3  ft,.,  „,„„g  A  N  a.d  3^8  lbs. 


Now, 


since 


these  forces  = 


Let  three  forces 


tant  of 


along  A  B, 


m 


100 


DYNAMICS. 


A  C,   and  A  D  (Fig.  D).    Let  the  angle  BAG-  60°,  and  let 

Draw  H  A  K  at  right  angles  to  A  C. 
Now  it  is  easily  seen  that  — 

The  angle  R  A  11  =  30° ; 
"        "     D  A  K  =  30°. 


Fig.  D. 


For  the  force  of  8  lbs.  acting  along  A  B,  substitute  its  re- 
solved  parts,  4  lbs.,  along  A  C,  and  4^/3  lb..  .  .long  A  H. 

For  the  force  of   6   lbs.  acting   along  .,      .    .ub«titutP  ifo 
resolved  parts,  3   Ibs.,along  A  C%nd  3  V  3  lbs   alol  I  K 

~  Ja  i^ilon^  A  u:  ^^^"^  ^=  ^'  -^  ( W3  -  3  V  3)lbs. 

.  -W-  .-^co  A  C  and  A  H  are  at  right  angles,  the  resultant  of 
o^  ':.  >p*  forces  =-■  V  ( 12  )^+  ( v'S  ;'^  ibs. 
»»VT47  1b8. 


COMPOSITION  OF  FORCES. 


101 


syli::iT\Zo:r''  "^^^'^  ^^"^^  ^'^  -^^^-^  ^^  oth. 


!•    Two  forces  each  of 
flml  the  resultant. 


QUESTIONS. 


50  lbs.  act  at  a  point  at  an  angle  of  60°; 
L  ^r?' "^  ^^  ""^'  2«  ^^'-  respectively  act  at  a 


point  at  an  angle 


"fGO°;  And  the  resultiuit. 

ataiiaugleof   fr,^;  anii 


4.    T»o  forces  each  of  e  lbs.  act  at  a  point 
the  resultant. 


6-    forces  ot  10  ami  12^3  Iba   rcsDeellvelv  .„,  .. 
angle  of  icoo;  And  the  resnltant      "*""'""'''  '«  "  «  !«"»•  «  an 

at  Tn  an'lJf  of'r""' "'  '""  ""•'="  ""'""'  '"  '"--""Sat.  -Int 

flnd'-thr^esfS. """  """'^  '"■'■  '"'  "  »  "»'"'  "  -  -«•=  of  "' 
lorce  oi  5  V  218 ;  find  the  angle  between  the  fcs. 

lb";  «l7;;ri;;f  °"^^"'"*  ^"'^"^•^  «^  ^^^-^  "-ir  resuuunt ,« lo 

,   .^^'    ^  ^^  "i^  i"  '^  ^'•°'"''"«   having  thr  angle  at  A  ^  coo-  A  D   C  R 
intersect  in  E;  fcs.  act  along  A  B,  A  D   A  E    and  R  v   ^  a  '  "^  "'  ^  ^' 

.lojea.othe.,„nan,.g„,t„ae„nhe,;'re!'„irt,^'^^^^^^^ 


>1 
i 


M 

m 


102 


DYNAMICS. 


^*'    The  resultant  of  two  eoml  fn=  „  *• 
1^«-;  find  the  components  ''*'"^  ^*  *"  ^°S'«  o^  135°  is  20 

15.    The  resultant  of  two  fc^  in   fi, 
-«Ieof  l50Oi.sO4„,,,  find  the  Ws        '''"   '''••''   ^^'^'"^^  ^^  - 

10.    The  resultant  of  two  fcs    artincr   .* 
one  of  the  components  is  9  Ibs.rflud  I'otLr"  "'''^  ''''°  ■'^  ''  "^•^- ' 

§  72.  Composition  of  parallel  forces       Tf  tr.     .  • 
and  CB  (Fig.  75)  are  brought  near  to  oTot  Tk  '*""^' ^^ 

ponded  from  B  and  E,  so  Ihat  t^e  ^no^ Vo  V"  "'^"^  ^"«- 
dimiuished,  the  component  force  nt^r  ™'^  ^^  *^^'"  ^« 
mometers,  will  decrease,  1 11  the  Vo  T  '"'''  '^'  "^^  ^^^"- 
when  the  sum  of  the  com  1     .  ""'"''  ^^"^"^^  Parallel, 

Hence,  (l),..,,J,t;3-2/;^^^^  ;^r  ""  ^^^^'^^^  ^^' 
ac^m^^a^e  ../.en  they  are  7arau!  a  ,  /''  "'' ''  ^^^e  greatest 
^^^ich  case  tkeir  reZtZ ^;:;^,::lZ  '''  ""^  '''''''^-^  ^^ 

oZ  '^::t::::t^:::T': '-'  -'-^'-^  ^-^  -h 

necessa,,  to  supp^i::  ^g^tc^^  n.!;^  'ITV''  '-"- 
actly  opposite  each  other,  when  the  two  ^"^'     ^^'"^  '•^- 

other,  and  none  is  exerted  T.,  „  ^^J  "  "'"*''"''"^  ''^'^' 
weight.  If  the  two  ^:i^:Z^''''''^  ^"^^^^^'-^  ^'- 
weight  (the  weight  bein?  sZ^oted^^^^ 

pulled  with  equal  force  ttSf?  ^  '  "'"'^  ''^^"^)'  '^^"^ 
is  pulled  witl'a  force  of  15  ZTl  \T  """  ^"^  ''  -« 
-•  10  pounds,  the  weigh^m^^ tlhTdi  e\^^^^^^^  ^  '^^ 
force;  and  if  .,  tliirf  dynamotnptm.  i,  !»    ,  '°  «''"'"«'■ 

the  .id.  of  tl,e  weaker  LT"      ol^Tl     "^  "°  "'='«"'•  <"• 
of  5  pounds  must  bo  anXd  ,1  ""''  ""  '"'<"'''""''  foree 

««o&r;  ldtk/ZTo}laJllf         "''"  ™'"'^<« /™™  »'« 
to  tteiV  di^cmice.  ''        ^"""^''■'iira.iJTO/iort/oMate 


COUPLE. 


103 


Fig.  76. 


When  i)aralk'l  fon-es  are  not  applied  at  the  same  point,  the 
qtiostiou  arises,  Wiiat  will  be  the  point  of  application  of  their 
resultant?    To  the  oi)positc  extremities  of  a  l)ar  AB  apply  two 
sets    of    weights,    whicli 
shall  be  to  each  other  vm 
3:1.     The  resultant  is  a 
single  force,   applied   at 
some    point    between   A 
and    B.      To    find    this 
point  it  is  only  necessary 
to  fnid  a  point  where  a  single  force,  applied  in  an  opposite 
du-ection,  will  prevent  motion  resulting  from  the  parallel  forces  • 
m  other  words,  to  find  a  point  where  a  support  may  be  applied 
so  that  the  whole  will  be  balanced.     That  point  is  found  by  trial 
to  be  at  the  point  C,  which  divides  tlie  bar  into  two  parts  so 
that  AC  :  CB  : :  I  :  3.     Hence,  (3)  ivhen  two  parallel  forces  art 
upon  a  hotly  in  the  same  direction,  the  distances  of  their  points  of 
application  from  the  point  of  application  of  their  resultant  are 
inversely  as  their  intensities. 

The  dynamometer  E  indicates  that  a  force  equal  to  the  sum 
of  the  two  sets  of  weights  is  necessary  to  balance  the  two  forces 
A  force  whose  efTect  is  to  balance  the  effects  of  several  ccmpo- 
ucnts  IS  called  an  equilibrant.     The  resultant  of  the  two  com- 
ponents is  a  single  force,  equal 
to  their  sum,  applied  at  C  in  the 
direction  CD. 


Fig.  77. 


§  73.  Couple.  —If  two  equal, 
parallel,  and  opposite  forces  ar*> 
ai)plied  to  oi)posite  extremities  of 
a  stick  AB  (Fig.  77),  no  single 
force  can  be  applied  so  as  to  keep  tlie  stick  from  moving ;  there 
will  be  no  motion  of  translation,  but  simply  a  .o.../on  around 
Its  middle  pomt  C.  Such  a  pair  of  forces,  equal,  parallel,  ad 
opposite,  but  not  in  ti.e  same  line,  is  called  a  couple. 


% 


(i 
»' '  ■  I 


III 


i  fil 


104 


15TNAMICS. 


1    A  PROBLEMS,    ETC 

2-  If  the  vv!    2^  ""^y  ^""PP^"  20^  ?  ^"'^  '^'^^"Id  "'e  weight 
each  s/ppttr'^"'*  ^-  P^-e.  4o™  ,ro.  «,e  .an  how  „     . 

3-  Suppose  thaf«h    .,  ""*"' ^^^^  much  would 

Wide,  ancHs  ro  ved  wlfh     '^''''"'  ^'"--^"y  across  a  H       . 
shore  in  half  an  hn        ?  '^  ''"'""'^y  »hat  w„„ici  lalufl    ""  ^^^^  «  '"'Je 
the  boat  down  th     T' ''  ''''''  '''''  "«  ^"rrtt '"'  '  "P^"  '^^  °PPo«ito 
".e  boat  land?  '''  ^'"^"^  ^'  *^«  -te  of  one  nJiie^  t^^'Z  ^^"^^"^ 

*-Howfarwiin.traveIP 
"•  How  long  will  ith^i 

••  A  ship  l/sail  IL^        °''°'''°S  "">  --iver? 
""r"  ;',:*;  rr;*^  ™'«""''"'  "'  "^  "''  "'  "• ""-  0"  "our, 

Venfy  the  rcsulta  With  ,„„.„„„,^^^ 

X.     OTHER  APPLICATIONS  OP  THP   =. 
Let  I  •  '""'•  -  ^™^°«  ™  OHA  V^  '^'^  °-  MO. 

-«^«^  measured  bv  fhn  ,„  •  ,/  "'^  ^^'''ce  is 

"ally  downward   ;"e    '7?  "*'"«  ™«i- 
-<1"«U  their  sum  ;,d, /"!,"'*""'  "f  "hi-'h 

position  the  My  XtZTJ^'^''' 

^/^Ae  rm^^a?^if  .,^  a//  fhZ  /  '"^^^Me,  the  point  of  appH.^f.-^ 
^hole  weight  of  the  hodu  mLZ  """  "''^"^  Purposes  the 

its  center  of  nravitu      W      ^        ''"^'■^"'^^  '«  ^'«  coL^L/;     ! 

'-U  that  point  Where  the  0.,^;^::^^^^^^^^^^^^ 


CENTEB  OF  GRAVITY. 


105 


'  Jong,  sup- 
tlje  weight 

luch  would 

»alf  a  mile 
3  opposite 
nt  carries 
''■Jiere  will 


>erhour; 

y  of  two 

i  weight 


F  MO- 

nee,  a 
force 
J'ce  is 
eciile. 
denies 
verti- 
vhich 
ction 
las  a 
;ever 
•oint 
•titer 
tiuri 
the 
'  at 
fa 


Let  G  in  the  figure  represent  this  point.  For  many  practical 
purposes  then  we  may  consider  that  gravity  acts  onl/upon  Z 
pom  ,  and  m  the  direction  GF.  If  the  stone  falls  freely  th  s 
pomt  cannot    in  obedience  to  the  fir.t  law  of  motion    de'v^^ 

LTall  "J'na  P'^^^  j— '  ^^^  the  body  may  rotat'e  durh^ 
Its  fa  L  Inasmuch,  then,  as  the  e.g.  of  a  falling  body  always 
descnbes  a  definite  path,  a  line  GF  that  represents  this  ".t .' 
o.  the  path  m  which  a  body  supported  tends\o  move,  is  cd^' 
the  hne  of  direction.  The  centre  of  gravity  is  often  called 
the  centre  of  inerUa,  and  this  latter  name  is  very  api^pri!  ' 
when  we  are  speaking  of  this  point  with  reference  to  the  ma  s 
of  the  body  instead  of  with  reference  to  its  weight.  (§§  7   19 

onnl  >  '• '^.'°'  *^'*  '^  ^  ^^'"'^  ^'l"^^  *«  ''''  «^«  weight  and 
opposite  n.  direction  is  applied  to  a  body  anywhere  in  L  line 

of  du-ect^on  (or  its  continuation),  this  force  will  be  the  equi- 

hbrant  of  the  forces  of  gravity ;  in  other  words,  the  body  sub- 

jee  ed  to  such  a  force  is  in  equilibrium,  and  is  said  to  be  sup- 

ported,  and  the  eqailibrant  is  called  its  mpportiru,  force      To 

support  any  body,  then,  it  is  only  necessary  to  provL  a  support 

for  us  center  of  gravity.     The  supporting  force  must  be  apS 

somewhere  m  the  line  of  direction,  otherwise  the  body  will  fall 

hemisphere  of  lead.     The  toy  will  not  *''^'  '"■ 

lie  in  the  position  shown  in  the  figure 

on  a  horizontal  surface  ab,  because         

^j— ..,  ..^  ,„,....  apphuu  immeaiateiy  *  v 

under  its  e.g.  at  G;  but,  when  placed  horizontally,  it  immedi- 
ately assumes  a  vertical  position.  It  appears  to^^he  o W 
to  rise ;  but,  regai-ded  in  a  mechanical  sense,  it  really  falls,  be- 


lli 


i 

M 
•''iii 


Urn 


i' 

U 


106 


DYNAMICS. 


cause  its  c.  g.,  where  all  the  weight  is  sunnnse.l  fn  h 

trated,  takes  a  lower  position  ^"PPOsed  to  be  concen- 

bounded  „v  the  string  is  the  ba     '7  lie  tb k      ^fvt  t    T 
base  of  a  u.an  whe,.  standing  on  one  foot?  ™  two  fiotP)       "' 

F!^.  80.  .ere  will  be  an  equilibrium  of  forces,  and 

the  e.g.  must  be  iu  the  same  line  with  the 
equilibraut  of  gravity ;  hence,  if  a  knitting- 
needle  is  thrust  vertically  through  the  no- 
tato  from  a,  so  as  to  represent  a  continua- 
tion  of  the  vertical  line  oa.  the  e.g.  must 
he  somewhere  In  the  path  an  made  by  the 
needle.     Suspend  the  potato  from  some 
^other  pomt,  as  b,  and  a  needle  thrust  verti- 
cally  through  the  potato  from  6  will  also 
pass  through  the  e.g.     Since  the  e.g.  lies 

their  point  of  Intersection.     U  win  Velurtl^  \T'  ''  ^*  '' 

§75.  Three  states  of  equilibrium.  -  The  weight  of  n. 
body  .s  a  force  tending  downward;  hence,  a  6oc^/w^  JJ 
sume  aposUion  suck  that  its  e.g.  null  be  as  low  as  pisWle, 

5  ^Tllrf.  '•  '''y  *.«  «"PP°''t  «  ring  on  the  end  of  a  stiolc.  a«  at 
c  >miau.     oupport  It  at  o.    Have  you  any  difficulty  hi  sup- 


STABILITY  OF  BODIES. 


107 


be  concen- 

^ther  or  not 
f  a  body  is 
3  of  a  body 
ng  around 
ular  figure 
^hat  is  the 
t?) 

body.  — 

tack,  as  in 
nes  to  rest 
brces,  and 
e  with  tJio 
!i  kuittiug- 
jli  the  po- 
coutiuua- 
c.g.  must 
^de  by  the 
'om  some 
rust  verti- 
will  also 
3  e.g.  lies 
it  be  at  c, 
ver  point 
mder  the 
is  found, 
le  of  the 


it   of  a 

s  to  as- 


ki  as  at 
r.  of  the 
imain  at 
^troyed, 
iu  sup- 


Fig.  81. 


porting  it  in  this  position?  Disturb  the  ring  and  remove  the  disturbing 
force.     Wliat  happens?    Why? 

A  body  is  said  to  be  in  stable  equilibrium,  if  its  position  's 
such  that  a  disturbance  would  raise  ite 
e.g.,  since  in  that  event  it  would  tend  to 
return  to  its  original  position.  On  the 
other  hand,  a  body  is  said  to  be  in  nn- 
Htable  equilibrium  when  a  disturbance 
would  lower  its  e.g.,  since  it  would  not 
return  to  its  original  position. 

A  body  is  said  to  be  in  neutral  or  in- 
different equilibrium  when  it  rests  equally 
well  in  any  position  in  which  it  may  be 
placed.     A  sphere  of  uniform  density, 

resting  on  a  horizontal  plane,  is  in  neutral  equilibrium,  because 
its  e.g.  is  neither  raised  nor  lowered  by  a  change  of  base.  Like- 
wise, when  the  support  is  applied  at  the  e.g.,  as  when  a  wheel 
is  supported  by  an  axle,  the  body  is  in  neutral  equilibrium. 

It  is  evident  that,  if  the  e.g.  is  bclotv  the  sxqjport,  as  in  the  last 
experiment  with  the  ring,  the  equilibrium  must  be  stable;  but,  as 
in  Figure  79,  a  body  may  be  in  stable  equilibrium,  though  its 
e.g.  is  above  the  point  of  support.     (When  is  this  possible?) 

It  is  difficult  to  balance  a  lead-pencil  on  the  end  of  a  flno-er ; 
but  by  attaching  two  knives  to  it,  as  in  Figure  82, 
the  e.g.  may  be  brought  below  the  support,  and  it 
may  then  be  rocked  to  and  fro  without  falling. 


Fig.  83. 


§  76.  Stability  of  bodies.  —  The  ease  or  diffl- 
culty  with  which  bodies  supported  at  their  bases  are 
overturned  depends  upon  the  hight  to  which  their 
c.  g.  must  be  raised  in  overturning  them,  and 
upon  the  weight  of  the  bodies.  The  letter  c 
marks  the  position  of  the  c.  g.  of  each  of  the 
ies  A,  B,  C,  and  D.  To  turn  any  one  of  these  bodies  over, 
its  c.  g.  must  pass  through  the  arc  ci,  and  be  raised  through  the 
hight  ot*.    By  comparing  A  with  B,  and  supposing  them  to  be 


rFiff.    8.S) 

\         c  -  -  / 

four  bod- 


um 


'n\ 


(i ' 


,'■:' 

111 

i  H^l 

n 

H 

HI 

108 


ni 


DYNAMICS. 


rmsed  high„,  and  &,  thereflTlJ^"^  J   "''''"'  ''«  """'  '^ 
A  comparison  of  A  and  C. ,7  """"' *™'^'- *»;«*» 

leases  and  Wghts,  but  D  ia  made  .1      ^  ?  "'"'  ^  '""">  ^l"*! 
'-«  -•'»  0.,.  „,  ,,„,,  ,  ^ -^^  ^-y  at  the  bottom,  and  Ibis 


Fiff.  83. 


1. 
2. 

3. 
4. 


QUESTIONS. 
Where  is  the  e.g.  of  a  box? 

•'0..0  Of  e,„.,  „eig„."r    '°  ""  '"""•""-<'.  «  '»«0  of  Hy  or  a  ,„„  „, 


CUEVnjNBAB  MOTION. 


109 


^ifght  and 
'  must  he 
difficulty. 
of  equal 
'  weights^ 
ve  equal 
and  this 


ontal 
iieij- 

sed? 


of 

in 


XI.  OTHER  APPLICATIONS  OF  THE  SECOND  LAW  OF 
MOTION. -CUliVILINEAli  MOTION. 
According  to  the  first  Ia^v  of  motion,  every  moving  body  pro- 
ceeds ui  a  straight  line,  unless  compelled  to  depart  from  it  by 
some  external  force.  If  the  external  force  is  continuous,  Le, 
acts  at  every  pomt,  the  direction  is  changed  at  every  point,  and 
the  result  is  a  curvilinear  motion;  and  if  the  force  is  constant 
and  acts  at  right  angles  to  the  path,  the  curve  becomes  a  circle. 

Thus  suppose  a  ball  at  A  (Fig.  84),  suspended  by  a  string  from  a 
po  „t .    to  be  struck  by  a  bat,  in  a  manner  that  would  cause  ir to  move 
m  the  du^cfon  Ao.    At  the  same  time  it  is  restrained  from  taking  that 
path  by  the  tension  of  the  string,  which 
operates  like  a  force  drawing  it  toward 
d.    It  therefore  takes,  in  obedience  to 
the  two  forces,  an  intermediate  course 
toward  c.     Atcits  motion  is  in  the  di- 
rection CM,  in  which  path  it  would  move, 
but  for  the  string,  in  accordance  with 
the  first  law  of  motion.    Here,  again,  it 
is  compelled  to  take  an  intermediate 
path  toward  e.     Thus,  at  every  point, 
the  tendency  of  the  moving  body  is  to 
preserve  the  direction  it  has  at  tliat 
point,  and  consequently  to  move  in  a 
straight  line.    The  only  .  ason  it  does 
not  so  move,  is  that  It  is  at  everv  nnint  fv...     i  , 
by  the  pull  of  the  string.     Bull     when  tt.    u      *"  "'  ""*"''"'  P"^" 

-..  i"  the  direction .,  which  i^  ii:^;;  I  i:zz  IX  S!'. 

This  tendency  of  a  body  moving  i„  a  curvilinear  path  to  fly 
off  ma  straight  hne  has  been  erroneously  attributed  to  a  sup- 
l)osed  'centrifugal  force,"  which  is  constantly  urging  it  away 
from  the  center,  it.  escape  being  prevented  only  b^  a  Tree 
pnlhng  it  toward  the  center.  ^  ^ 

Centrifugal  force  has  in  reality  no  existence ;  the  resulte  that 


pi 


« 


k4J 


!1; 


I' 


110 


DYNAMICS. 


line.      Th  s  Tv  t  r        r  '  *"""  ''''''^■■'"™  '-»  "  ''-i^ht 
.evolutions  are  Z! "'  t'"?  *'''  '""■''•      «•  "h™  30 

'".00  wiu  JCi7  o^ie'';:;::  x^  '^r'-t^-  "■' 

-d  tho  velocity  regain,  o/Za    thi    ftTCf 'J/°:r/ 

f«e  square  of  the  velocity  increases  and  n^  fh^ 
increases.  «■<"  etweif,  ana  as  the  mass 

velocity       HantLLr?.  co„sa,„ently  the  greater  its 

the  g-eatast  tender  0%    ffC  2'"°%'"' "r"'"^"''^ 
whichistonentraliJin  ""'^°'*'  ""«  "f*"*  <>« 

is  oai^uiated :,::  i::,;"„:!rart\?  'T.r  *'"^''^- " 

Hfc  either  nnl^  ,',,  ^  ^*^  ^^^^  ^*  *h«  equator  than 

earth's   velocity    wefe   in  .        ''"""  °^  17;   hence,  if  the 

equator  .oul^^eiirLrr       ^^^^"^-^°^^'  <^^>«^«   ^^    ^he 

nnZ^-  '"''"  ^^'"^  ^'"'^"^  ^§2^>  *^^*  ^  body  weighs  more  at  th« 
poles  in  consequence  of  the  oblateness  of  the  eartk     TM  . 

.«ated  to  make  a  difference  of  about  J      S!  \     ""  ""'"' 

weigh  at  the  equator  about  ,^,71  -    ,^7^\^,  ^^^^^  -» 
poles.  "  ?8?J  +  2*Tr  -  Tk  less  than  at  the 

^Mis,  .    ,.a,i„ar,  straight  n„e  pa«.„,  through  a  bod,  about  which  H  roiat^a. 


!:fi 


QUESTIONS. 


Ill 


Experiment.  Arrange  some  kind  of  rotating  apparatus,  e.g.,  A 
I'ig.Si.  Suspend  a  skein  of  thread  a  by  a  string,  and  rotate.  Sus! 
pend  a  glass  fish  aquarium  e,  about  one-teuth  fuU  of  colored  water  and 


rotate.    Pass  a  string  through  the  longest  diameter  of  an  onion  c,  and 
rotate.    State  and  explain  the  result  In  each  case. 


QUESTIJNS. 

rofatedT''^  '^°''  "''^  '^'  '^''"■'  ^  ^^'^^  ''^  '''"""^  '''  P°«^"""  wl>«» 

2.  State  the  various  facts  illustrated  in  the  act  of  slinging  a  stone. 

3.  («)  When  will  water  and  mud  fly  off  from  the  surface  of  a  re- 
volving wheel?,  (i)  Why  do  they  fly  off?     (.)  lu  what  direction  do 

theh"  orWtsJ  ''  *""'  '"'■''  ''''*  ''""''"  *^'  '"''^  ""^'  ''''  '''''''  l'l^"«t«  in 
5.    How  do  you  account  for  their  curvilinear  motion  ? 


ti± 


mi 


I 


nm 

11 

'  1 

11 

''11 

^11 

ill 

n 

H 

'tH 

1  1  WH 

1:1' 

M 

'1*1 


112 


!  '^    ! 


I>YNAMlCa. 


5  77.  Accelerated  „„«o„  „,  ""'™''- 

™se  of  motion  „„,er  ZI^LZt^T^-^  ""'  "«'  "->y 
''7  «t"diccl  is  .h«t  of  curv  llear  l^"""""^  '""c  that  „e 
"«ta  at  an  angle  .„  the  <lircc  to"r„.r  "'  '"  ""''=•'  "■"  '"■« 
and  so  tl,»  ,li,.ection  of  «,.  1?™  "'°"°"  "'   '■'">•  Point 

*e  motion  Ukcs  piaoe  ^1:^^: ZS^v'  '"^''^''^'  ""'  ^' 
•he  forec  acts,  we  simll  have  one  of  ,  J  '  "^  ""'  '"  ""'"I' 
"^fcned  to  in  §  67.  °'^  ""^  '^''^^  <>(  varied  motion 

aWo^rr!,!:;;;:™' j;;';j^';'^';"«'  «  l-«vy  car  we  „V  be  u„. 

ti.ey  continue  to  JenlZJl'T,,"'  """^  "=»»<'«!  bnt,  ^f 
greater  and  greater  veloeitrnnt^L  t T  ''  "'"  "'°^«  ""'■ 
creases  with  the  velocity)  hec^^e,  !      ,       °®  '*'™  (""ch  i„- 

,7°-     This  continually  incrrir.!",     T  """  "'"Jied  by  the 
ated  velocUy.  "  ""'"^'•'S  velocity  is  tenned  aaeler 

fr^t-stovy  window.     Inasmuch  as  T    .    ^"'^  ^  J""^P  ^''^'^  » 

«  «o  great  tl.at  there  is  not  1 1  ?«    '  ''^'f  ^'  "'  '^"'"^  ^«^'es 

"'-r  fall,  we  must  resort  to  si„eT?1  '''''''''''''^  ^'"-'"^ 

vcIoaty,witlK>utotherwisectn:n:the   r  ''  ^'^^''"»"  ^''-^ 
E-Per,„,e„t     Tak.  '""^"^^  "'« -'^-•'-eter  of  the  fall. 

higher  than  the  other.  Sus- 
pend within  easy  view 
a  string  (about  lmio„„-) 

anddr"''*'"-^^"'*"'"'"' 

Vibration,  and,  at  the  instant  th«  h„n  ^®''  ^^^  ball.    Set  iMn 

to  roll  down  the  inclined Xe  '  r  ^t  ^  "T''  ''^ ''"''  ^^*  «  ™arb5  b  '  1 
hoard  thatthfi  ba!i  rearh       !"   ,    ^*"°*^er person  mnru  .}.„".  ®  "^^'^ 


^ijf.  8a. 


ACCELERATED  MOTION  OR  VELOCITY. 


113 


at  the  end  of  the  second  and  third  swings;  also  verify  the  precedlniF 
points  by  several  trials;   If  there  Is  a  difference,  take  the  mean  Z 
tanee  between  the  points  obtained  at  the  end  of  a  given  swi,  gTor  In 
Uproxlmate  result.     If  the  experiment  Is  conducted  with  car^  lty.ni 
e  found  that  during  the  first  swing,  which  we  call  a  unit  of  time  (T) 
the  marble  moves  through  a  certain  space,  which  we  represent  by  the 
xi>re  s>on  J  A-;  during  the  second  uult  of  time  it  moves  throu-^h  ^k 
luoo  t.mes  the  space  that  It  did  in  the  first  unit  of  time,  and  durin.: 
tho  tlurd  unit  of  time  it  moves  throu-h  ;]  k.  " 

^^^Arrange  the  results  of  your  obsermions  in  a  tabulated  fom  as  fol. 


No.  of  units  of 
tiiue. 


Total  distance 
passed  over. 


Distance  passed    Increase  of  ve- 
over    In    each        locity  in  each 


1 
2 
3 

4 
etc. 


unit;  also  av- 
erai/e  velocity, 


1  (U) 
4     " 
9     " 
IG     " 
etc. 


3    «' 

5     '< 

7    " 

etc. 


unit,  i.e.,  «c- 
celeration. 


Velocity  at  the 
end  of  each 
unit. 


2  " 
2  " 
2  " 
etc. 


4     •' 

G     " 

8     " 

etc. 


The  marble,  under  the  influence  of  gravity,  starts  from  a 
state  of  rest,  and  moves  through  one  space  in  a  unit  of  time. 
Gravity,  contmuing  to  act,  accomplishes  no  more  nor  less  dur- 
ing  any  subsequent  unit  of  time.     But  the  marble  moves  throu<.h 
tiiree  spaces  during  the  second  unit;  hence,  two  of  the  spaces 
must  be  due  to  the  motion  it  had  acquired  during  the  first  unit. 
In  other  words,  if  the  action  of  gravity  were  suspended  at  the 
end  of  the  first  unit,  the  marble  would  still  move  on,  and  would 
pass  through  two  spaces  during  the  second  unit.     It  therefore 
has  at  the  end  of  the  first  unit  a  velocity  (V)  of  two  spaces  (k\ 
per  unit  of  time.     But  it  started  from  a  state  of  rest ;  hence  the 
constant  action  of  gravity  causes,  during   the  first  unit,   an 
acceleration  of  velocity  equal  to  two  spaces  (fc)  per  unit  of  time  • 
and  It  causes  the  same  acceleration  during  every  subsequent 
unit  of  time.     The  distance  k  [.  called  the  acceleraiion  per  unit 
of  time  in  a  unit  of  time,  due  to  the  constant  force.  A  body  im- 
pelled by  a  single  constant  force,  and  encountering  no  resistances 
always  has  a  uniformly  accelerated  motion.  ' 


'I- ■ 

!lff| 
1 


:  :.!t  m 


114 


DYNAMICS. 


f "i4r  n::^r  r;r:::  rr " '^r  •  - 

Let  M  =  measure  of  initial  velocity. 


V  = 
.s  == 


ii 


n 


k( 


U  -)-  V 


final 

aeeelcmtion. 

time  of  motion. 

(listjinee  traversed  in  time  t. 


X    t 


But 


X  t 


mi?anIk°n°dyL«ef' Tf  '°'^  independent  of  its 

"""I.  soem  as  tkougl,  a  I.eavv  bo,,,,  fal  r,  ,st    „ 
a  lio-  it  hnrlv      n„Ti  -^  raster  tljan 

'^iit  bo(h .     Gal.leo  was  tlie  first  to  si.ow  tl.o  falsitv 
of  this  assumption.     He  let  rlmn  f..^  ^        ^ 

iron  balls  of  ^iee        /'''."-^  '""P  ri'oin  an   eminence 
"uij  uaus  ot  difrerent  we  (I- Its  .     fi,,„,  „ii  ,     ,     . 

ground  at  the   same   instan         ir!   ^  """"^''"^   ^^' 

that  the  velooityoTa  Z        )  '  ''"  concluded, 

mass.       (Thi7cXb rf  e^  ''        '  ''  "'^^^^^^^^^-^^  «/  ^'^^ 
ueated  h  ^^^^''"'-^ted    experiment    should    be  re- 

ideated  by  every  student.) 

He  also  dropped  '.alls  of  wax  with  the  iron  balls 

Uie  iron   balls  reached   the  ground   first       A 

.nds  Of  matters  affected  mort  stro  J  t  .  '     .^ 

than  others?     If  a  coin  o,ul  o  f    .1  '   fe'-i^Xation 

longgUss  tube  (Fi..  87     and    ,'  T        "'''  ''^''''''  '"  ^ 

turned  end   for  end    I       -u    u  ^'^''^^^"«ted,  and  the  tube 

-.  end,  ,t  W.11   be   found   that  the  coin  and  the 


RETARDED   MOTION. 


115 


feather  will  fall  with  equal  velocities.  Hence,  gravity  attracts 
all  matter  alike;  but,  iuasmuch  as  a  wax  ball  presents,  accord- 
i»g  to  the  amount  of  matter  in  each,  more  surface  for  resist- 
ance of  the  air  tiian  an  iron  ball,  it  falls  more  slouly  We 
conclude,  therefore,  that  all  bodies  fall  with  equal  xelocities  in 
a  vacimm. 

When  the  body  falls  freely,  and  the  unit  of  time  is  one 
second,  we  use  the  letter  g  instead  of  Jc  to  represent  the 
acceleration.  Experiments  show  that  in  the  latitude  of 
Ontario  the  value  of  g  is  y.8-,  or  about  32^  ft.  per  second  ; 
that  IS,  tne  velocity  gained,  if  the  force  of  gravity  acts  one 
second,  is  9.8-"  per  second,  and  the  body  would  fall'ln  the  first 
second  4.9"',  or  16-iJj  ft. 

§  80.  Retarded  Motion.  —  If  we  reverse  the  order  of  the 
hgur.'s  in  Fig.  ««,  tlie  same  diMgram  will  represent  the  motion 
of  a  body  rolhng  upward,  or  tiie  motion  of  a  body  under  the  in- 
fluence of  a  retarding  force.  The  formulas  given  (§  78)  for 
finding  velocities,  etc.,  of  bodies  having  uniformly  accelerated 
moti.;n,  nn.y  be  used  for  linding  velocities,  etc.,  of  bodies  havin.^ 
undormly  retarded  motion  ;  but  in  the  case  of  uniformly  retarded 
motion  Jc  is  negative,  and 

V  =  u ~k  t 
.'  .    .s  =  a  t—h  k  t'\ 

Of  course,  if  the  acceleration  begins  when  the  body  is  at  rest, 

n  =  o. 


u 


the 


PROBLEMS. 

(Solve  these  problems  from  1  to  12  i„  both  the  metric  and  the  English  measures.) 

1.  Disregarding  the  resistance  of  the  air  what  distance  will  a  body  fall 
from  a  state  of  rest  in  five  seconds  ? 

2.  Wiiat  distance  will  it  fall  during  the  fifth  second  ? 

3.  What  is  its  velocity  at  the  end  of  the  fifth  second  ? 

4.  A  stone,  dropped  from  a  balloon,  strikes  the  ground  in  seven  seconds 
xlow  higri  is  tiie  balloon  ? 

6.    Under  tiie  influence  of   a  constant  force  a   body  moves   from  rest 
500'"  m  a  minute.     How  far  will  it  go  in  an  hour  ? 


116 


DYNAMICS. 


8-    A  bodv  f..liv  f..        '*-  """"«^  t'le  flfty-niiith  niinnte? 

'-« -teJt^u  to  :;;;:;:r;;sr '"^"^^^^""^^ 
«.  What  is  it.  cf!:,  x;;^  j^r'^^f  r'"'-  "'^  ^--"^^ 

^0.    What  is  its  vortical  vol,    tv  af  tho       T'r    .  ""  '""'•^"  ^^^^'^'^ 
"•     With  what  vertic-il  vol,    i^  ""'  ""^  "'^^  ^""'•^''  «^'C">h1? 

tl.ree  seconds?       "'"'^"^  ^^'^'^^'*>'  '""-sta  body  start  that  it  may  ascend 

^er  second ;  when  and  wlie  e  w  '        "'  '''"'  '  ''^''""'^^  "^  -'^"'-^  ^■^- 

14-     In  Que  f       1'     .  "'*^  stones  meet? 

when  and  where  wouk.  theThave"met-r''  "''"  ''"'''''''  ^«>vn wards, 

a  velocity  of  200  ft.  per  second  Twt."^.''"''*"^^""^"''^^ 
after  the  first  stone  slarted  '  "'<^"' ^ 'stance  apart,  4  seconds 

ou^-  a^;r  if  dr;:;;d'xrt'"r  '?^^  *^^  ^^  ^  ^--  ^  «- 

as  to  overtake  the  othe'  in  ;  Tecond!?  '''  ™"''  ^'  '^  *^^«^°  «" 

17.    How  high  will  a  body  rise  wbiol,  i=  f. 

seconds  from  starting.  ^^locity,  fl„d  the  space  described   i«  g 

-o';.Avr.taf rr,:,rwuM;:''vrr'r "  ^»» '-'  -- 

ond?  »'"  ^^'"  "s  velocity  be  80  feet  per  see- 

20-  A   stone  fallinL'  from  rest  fn,.  f 

»-'e  Of  glass,  thereby^losinTone-  h  :i  of  Tts"T"'r  '"""  ""'""^'"  ''^ 
^'.-ound  three  seconds  afterwards    find  fh   f  .^f^'^'*^'  «"^  reaches  the 

21-  Gravity  at  the  surf-  0^0^ .?       ,     ''"'''"'*  "^  ^'^'^  ^'"««- 
timesasgreatasatthesurftceof  tt  '  71  "■"^'^'-  ^^"'^'  ^'-"^  ^^« 
a.K,  velocity  acquired  by!    4"TaC' /"'«'" ''^^^'"^  ^••---'^' 
Jupiter  from  a  point  near  its  surface         "^  ""  '""""^^  *°^^'"'^'« 

pe:ict.n::,L^:r;:::;;:;;^:- -^  ^^nu.  veio^ty  of «« .et 

second,  how  high  will  ft  rile?  '""^  ^'  ^'''  ?«''  ««^«"d  per 


hour? 

i ;  meantime 
■  ill  a  liori- 
lie  gromul? 
I'th  socorul? 
secoiul  ? 
way  ascend 


ft-  per  sec- 
Jf  22r>A  ft. 

'vvnvvards, 

•  per  sec- 
ards  witii 
I  seconds 

er  3  sec- 
lirovvn  so 

upwards, 

lass,  and 
iJed  in  6 

feet  per 
per  sec- 

roiijLfli  a 
!lies  tlio 

out  2.6 
iversed 
awards 

CO  feet 
Jd  per 


PROJECTILES. 


117 


>.a«„„«  t,„.„„,.„  a  Stopper  at  I,  a,,.,  i„.  r.  JZZ    f  SZ''"^ 
Keep  tho  can  /i]|e,l  with  water,  lien.l  tl,e  lower  mttlriZrll      ,  ?' 

int'l'^'of  'J'""'"!""' J"",""™  "  "■'"'""™  representation  of  the 
fr2„?  ,  .'"■''J™"''^^''  »"«■>  »»  ea„„o„.baIls,  stones  thrown 
ftom  the  hand  etc.  The  horizouUtl  distance  that  the  proJectUc 
atoms  ,s  called  its  n«^.  „r  ra,ulon..    Theoretically,  the  gteat! 

o3'«  *"?"  "'  ""  ""°""  of  «°^  "•"  l»otiealf    on 
account  ol  the  res.stanee  of  the  air,  it  is  at  a  litUc  less  than  40". 


Fig.  88. 


M^v. ty,  and  (2)  tho  resistance  of  the  air.     It  also  has  a  eertiin 
velocity  and  direction   at  the  instant  of   projection.     If  this 
velooty  and  cJirection  are  kno.vn,  and  the  resisfinoo  of  th'  .ir  L 
cl.sregarded,  the  path  of  a  j,rojectiIe  can  he  determined."  ^TI^, 
suppose  that  a  projectile  is  thrown   from  A  (Fig.  89)  at  an 

♦Projectile,  a  body  thrown, 


III 


M 

u 

11'' 

I' 

*!■■ 

I 
11 


#1 


118 


bs.t 


DYNAMICS. 


eively,  are  B,  C  and  n     V,   ,  ""'  ""'^'=  "»''«  ^ucces- 

unite  of  tim«     TheTr  J'  "'' "'  ^°"='' »'  ""^  ««'  'hi-ee 

curved  iJaB'^"D"  Tne'^tr'T?'''?"'  ""'^^  ''""^'  ''-= 
"e  equal,  it  must  reaeh  i*f  .  "'  ""^  ""«'"'  "'«'  <'<^'«»»' 
the  tWrd  ulit  wll„  -M       *'■''"'"  ""■''■="'  ""Sl't  at  tl:e  end  of 

D'm"t  round  If "  •',  """•  '"■"  '"'"■  »'  <•-'=«"• 
acribed  is  known  as  a  1  .'";  ""'  '"''""'"■-  '^''  P=""  ">"«  "e- 
praetioaily  „r„::';rthe      'T""'  "•"'  '"»""«"  as  this  is 

describes  a  Xtr  Ih  .   r^T  "'  ""  ""■'  "  ">  '-'i'^ 
'     """  P"""  """sd  a  bmstic  curve.    Tlie  curve 


rtf.  89. 


-Ut  „ou.d  cause  it  to  .aerJ^a^tCd^^rttl.^S 

in  XlTllT^T"  "'■ '""  ''"""  '^^  »'  "■<"'<»>  -  'o„„d 
ground  rprue,;rirr''''',''°"^°"'»''^'  ""'  '■-«''  «■« 

mot  nn    o    1^.J,.  u  .  '"o'Jt"        inat    IS,    nUV    previnna 

o7gravity:^u"u:  'L^;!  *'■"'""  '""^  -'"  ^^'^^  ■"'^  -ti"" 


ind  that  the 
nits  succes' 
inimpeded, 
that  direc- 
Combining 
)",  reached 
!  first  three 
to  change 
units,  the 
id  descent 
;he  end  of 
of  descent 
I  thus  de- 
as  this  is 
in  reality 
'he  curve 


wn  from 
velocity 
I  unit  of 

8  found 
ach  the 
3d  from 
Tevious 
action 


H^VESTIGATION  OF   PROJECTILES.  119 

thf  f  "^^'^r*  '^'  ^"PP^'*  *'^^  ""^^  ^^'''  «  ^"f'  ^  (Fig-  90).  bent  into 
Zl  doTn  H  '  ""'T,^' •^'^«»*  ^"■"  "P-*.  a-'  -  ^ituatei  that  a  ball  n.   oil 

So  conl  r*  "^  '  ^  V'"''"'"^^'  '^""^  ^'^^"^ '"  *  horizontal  direction. 
So  connect  the  wires  of  an  electric  battery  .  with  these  bars,  that  while 
the  non  ball  n  rests  upon  them  the  circuit  is  closed,  and  the  iron  ball 
m  .s  supported  by  the  attraction  of  the  electro-magnet  e.    Now  allow 

broken  T  ".T  T"""'  ^^^'^  '^^""  ''  ^^^^  '^^  ^^  ^^e  c7rcu?'^ 
b.oken,  e  instantly  loses  its  power  to  hold  m,  and  m  drops.    But  both 

balls  reach  the  floor  at  the  same  instant.    If  the  horizontal  velocity  of 

Fig.  90. 


n  is  varied,  by  allowing  it  to  start  at  different  points  on  the  bars  so  as 
to  cause  it  to  describe  different  paths,  the  two  Lis  wm.  n  eve  y'   ase 
ac.qu>re  exactly  equal  vertical  velocities.   This  experiment  marbe  varied 

Shan  contain  the  Imc  of  direction  of  the  ball  m.    If,  in  this  case  the 
balls  are  far  enough  above  the  floor  at  the  start.  what'si^ouM  h„;p;„$ 

§816.  Investigation  of  Projectiles.  Continued  -In 
mvest.gat,ng  the  paths  of  projectiles  we  shall  find  it  oontniPn" 
to  consider  the  horizontal  and  vertical  motions  separately 

If  we  neglect  the  resistance  of  the  atmosphere,  which,  for  the 
sake  of  simplicity,  we  shall  do,  the  horizontal  motion  is  a  uni- 


[ 


li; 


■J  .tin 


120 


m 


!    '  ! 


DYNAMICS. 


veloeu/  :::;  :::n  j;;;;-f        -  the  inula,  absolute 

the  direction  of    1     ,   ot Uo     7  'l-   ""  ''"  ^'  Projectiou), 

point  of   path,  the    al     h  '      '    ""'  "'  ^*«'^*'  *^«  '''S^^  ' 

-moment  after  ^ro  ee  ior;„     t,"'''''^''/^'''^'*^  ^'  -»3^  g'>o„ 

any  given  mor^nt::^;^^^  ^^^'^^  ^^  *'-  P-J-tile  at 

TJ.e  horizontal  veloci  v  -  --      "f  .'  "'  '""  "^«^'*^  «'«  ^'orizon. 

"    initial  vertical  '       ^  Z  ll'  ^'  '^^^  ^''  «««o'k'- 

The  acceleration  due  to  LM-avitv'- •v>i  f"  *  "        "        ^§  ^'*)- 
ond(§79).  feiaMty  =  .]2i  f^et    per    second   per  sec- 

The  ball  will  continue  to  rise  until  fl>„  o  f 
vertical  velocity  to  zero,  an,  n       ""''T  "'  ^"""^'''^  ''^'^"^^^  '^s 

strikes  the  plane.  Sinc^  its  o  lei ,  '/""'' '''.'^'  '''  '"'^'^'^^  ""til  it 
dnring  the  fall  as  well  asduH  .  ,  e  j  t.r;"  '"i"'""""'  '^>'  ^'^^'^y 
as  the  time  of  rising.     (§§  78,  80.)  '     ""       ^''"'"*' ''  '"^  '^"^^ 

Hence,  the  time  of  flight  =  I!?  >,  o       ,,, 

32^  -^  -^  ==  *'^  seconds. 

^    To  tl„d  the  highest  ^oint  <  f  paH  S:'  T      l'^'  ^  ''^^  ^-^• 

1-ving  an  initial  upward  vertior  v  i^v  ^ 'l:^  V"  -'-"  '^  -ly 
rise  in  24  seconds.  ^eiocitj  of  n  2  feet  per  second  will 


Therefore,  highest  point  of  path  =  772  x  24 

=  92(J4  feet. 


32,i 
2"  X  (24)' 


Tc  And  the  position  of  the  ball  nt  th^       ,     . 
;i^ht  at  .his  moment  by  cc^.  i      ,t  it^  T^^''  ^^^.""^•'''  «»^  '^s 

itshonzontalpo.itionatthe.samemo  u.nfL  M   """'""'    '"'"^^  ""^^ 

motion.    Having  its  hight  and  W       V      ^  ^'""'^''''"■i"?,'  its  horizontal 

tionisofcour.se%xed.^;;^:i'thi:lu't.       ""'''"''  "'^  '^'^'^"'"'^  P-' 


SECOXD   LAAV   OF  MOTION. 


121 

To  find  the  absolute  velocity  of  fho  haii  „*  ♦!, 

square  the  ,neas„re«  of  its  veftic  U  td  !  f"'^  *''  ''  ^^^°"^«' 

moment,  and  extract  the  squa     "oot  of    th?"    "'  T""'"''''  ^*  *^'« 
Why?  '      ^  '°°'  °^    the  sum  of  these  squares. 

The  horizontal  velocity  is  uniformly  772    /'^  fn»f 


QUESTIONS. 

1-  A  particle  is  projected  at  an  an-'le  of  450  wifJ,  f ho  1,     ■ 

a  point  on  a  hon/..,ntal  plane  witi.  T 7-7  .  ^'th  the  horizon  from 
Find  its  range,  an.l  ftnc  ts  dist'Zl  V  ?'''^  ^''^^  ^'''  ^''  ««««nd. 
e.Kl  of  5  seconds.  "''  ^'■^'"  "'«  P°'"'  "^  projection  at  the 

2-  A  particle  is  projected  at  an  an^le  of  fino  f..«.., 
horizontal  piano,  and  its  total  range  is  5  000  feet     JuT-  If"'"'  ''"  " 
of  projection  ?  '       ^^^*-    ^^^^^^  »s  the  velocity 

3      A  particle  is  projected  at  an  angle  of  Sfto  f^nm  n       ■  . 
horizontal  plane,  and  tho  l.i.ri.„.f      •  .  !  """^  *  Po'"<^  on  a 


j,i 


'  ''■! 

Ill 
m 


Xiri.     OTHER   APmCATIONS   OF  THE   SECOND  LAW   OF 
MOTION. -THE   PENDULUM. 

in  F^7er"*D;aw'ira";ul  o"'*"''',  f"^^""'  '^^  '''"'''  '-'^-^  h«"«.  as 
B  xna; swing  tl^Z^H ^^^^ :^;  iT  .f  ''''"^"'  '''^'^'^'  ^  ".at 
C  moves  n.nch  faste    tharB  '  id  ^1      .  .      '?"  "'  ''"'  '^""'^  '"«*'">t- 

swing,  hnt  hoth  ^o..j^;;::,:T:^z:i^^jr'''''''  ^*  -^'^ 

•iio,  ui  viuration,  In  the  same  time. 
Hence,  (1)  ««  „•„;«  „„„pi„„  ,    „,^  ««**,» 


122 


DYNAMICS. 


■-  "^    (I 
"   ■■   i! 

'■      V. 


Bay  this  law  be  regarded  as  practically  trae.    The  pendulum 
or  a  short  one,  but  the  difference  becomes  perceptible  only  when 

.trrrortrt  ir„,r  :.r--  ^  -^ = - « sw,„,  to. 


Fig.  91. 


^'eiher;  the  shorter  the  pendulum,  the 

faster  it  swings.   Make  B  im  long,  and 

F  ,m  long.     Watch  in  hand,  count  the 

vibrations  made  by  B.    It  completes 

just  60  vibrations  in  a  minute ;  in  other 

words,  it  "  beats  seconds."  A  pendu- 
lum, therefore,  to  beat  seconcls  must 

be  im  long  (more  accurately,  .993™,  or 

3J.09  m.).     Count  the  vibrations  of 

i  ;  It  makes  120  vibrations  in  the  same 

time  that  B  makes  60  vibrations.  Make 

G  one-ninth  the  length  of  B;  the  for- 
mer makes  three  vibrations  while  the 

atter  makes  one,  consequently  the 
time  of  vibration  of  the  former  is  one- 
third  that  of  the  latter. 

Hence,  (2)  the  time  of  one  vibra- 
tion of  a  pendulmn  varies  as  the 
SQmre  root  of  its  length. 

1    W^  .  QUESTIONS  AND   PROBLEMS, 

two  vIlTOtlons  per  ml„„te?         '""""»"  '°  '"■»  »ecoud,?    Tliat  makes 

§  82,  Center  of  oscillaf  inn 
hollo  „...-,        ,  »Jo«-uiaT;ion.  —  ExnAritnpn*  i     «-,^    ^     , 

"••!i.^,  at  intervals  or  IS*;"'  bv  Dassintr  o  ,.,;  •  7,  "*""*•  *■    ^^untiect  six 

mannerof  pendulum  A.     TWs  forms^a  /     '    "™"^^  "'^'"'  «'^«'-  ^^e 

forms  a  compound  pendulum  composed 


I  pendulum 

ration  than 

only  when 

after  many 

C  swing  to- 


CENTER    OF    OSCILLATION. 


ry  as  C? 

?   Quar- 
t  makes 

ons  per 


ect  six 
ter  the 
upoaed 


193 

actuated  on  v  bv  tho  hnii  r  u  .„^  1^    -u  ^       "^^^    "  ^  "^ere 

ball  a  were  free  wo^  d  U  'J'/"*'  '"  ""'^°»  ^'''^  ^^  ^^  the 
constrained  to  ml'toLher    tlT?  7'"'  *'""  "^^  ''"^'  ^^  ^^«>^  -e 

motion  of/,  and  the  tendencvof^'  ^'  '-"'1  ""'  "^  ''  *^  '"''^'"  "^^ 
is  quickened  less  than  ^  and  J  ll  ..'  ''''  *^'  "^'^"^^  ^^  «•  B»*  « 
Checked  by  /  less  than  a,  and  c  e sTtha:";^  lUs^'^  ^^'^^  '^"''  ^  '^ 
must  be  some  noint  hot  JZ.         f  !  '^  apparent  that  there 

ened  nor  checked  by  thoonmV  Z  ^',^'"''  ^"'"^'^^  '«  "^'^l^^"-  'l"'^^- 
it.  and  where  ?  ^s w,eC  "'"^  °'  *^'  '""^  '^^^^^  '^"^  "elow 
number  o/':^^t:^::;i^^  ir''  '"^^^  ''^  -™« 
does.    Shorten  nendnlnm  n      Ta  ? l  ^"^  compound  pendulum 

i«  called  *r«r„7Sir  ""^  *' "'"''°''  ■>"'■"•  ™» "<"»' 

whose  lengk  .,  .j„a(  to  rte  &<*<.nce.  6e,„«,  „«  cenlerofoZl' 

center  of  oscillation  detennmes  the  rate  ot  vibration,  wlienever 
toe  e.pressio,W.^«  o/„™«„»  i,  „,«,,  it  ™„st  l,o  nlrlo, 
to  m.a„  tlHs  distance.    Strictly  speaking,  a  simpU  peM^, 

couise  sna  a  pendn  „m  cannot  actually  exist ;  Init  the  leaden 
JV,«,     Ml,  suspended  by  a  thread,  is  a  near  approximatLa 

ffp:e™t-„??j;.sro^t%r^^Lr£! 

flud  the  center  of  oscillation  ot  the  latu  to  be?    At, 

r::pr:rTr„;e'tii'ir£ 
^n.tirtirc\u;:ros=io-.f.-r 

lowered  by  the  addition  of  the  weisrht      Mnvl  T      7  . 
up  the  lath;  the  vibrations  are  quickened    ?What  Tthe  offl       f 
pendulum  bob?)  ^    ^^  '^  ^'^^^  o^^^e  of  a 

Experiment  3.  Remove  the  weight,  bore  a  hole  through  the  lath  at 


lii 


ii»\ 


i24 


DYNAIMICS. 


vibrate  about  the  needle      CoZ  rn    ^  "'"."f^"''-     ^ause  the  lath  to 

its  period  Of  vibraru  When  suspended  T        ^^  ;'''"'^'""  ""^^  -'"' 
Can  you  explain  it?  «"«Peiided  from  A.    What  is  the  result? 

You  have  virtually  two  pendulums,  B  C  and  C  A      n.  ,, 
in  conjunction  or  in  opposition?  ^  and  C  A.     Do  they  vibrate 

changeable,  m  other  words,  there  are  always  two  points  in  a  eo^n 
pounapenaulum  about  which  it  will  oscillL  in  tZZZr' 

t  J      "^T^  "  P"''""^  "'-^y  ^^  fi'^^^'^g  the  center  of  o  c  I'la- 
tion  and  the  equivalent  length  of  a  compound  pendulum      Fn^ 

same  number  of  vibra-    ^ ^' 

tions,  in  a  given  time, 
as  from  its  usual  point 
of    suspension :     that 
point  is  its  center  of 
oscillation ;     and     the 
distance  between  it  and 
the  usual  point  of  sus- 
pension is,  technically 
speaking,  the  length  of 
the  pendulum.     It  will    wmi^i^^^^m 

strike  It  horizoiifilly  near  it,  „„,,„...  ""'""""os,  and  wfih  a  cU,l> 

■nove,  ,„  t.e  ^^rJZVTZ::TZ  OsTatX  °'  "■"  '"" 
causing  a  sudden  ierk  on  thp  «*..,•«„  ,  •  .  .  ^"  ''  ^^  ^^^^  *'»™e  time 
the  lath  in  the  san  directti  n  ar  it^'f  ''  ''''  '^  "'^  ^'^"^-  Strike 
of  the  lath  now  mov^sfn  „  d  ^    V  """'  «^tremity;  the  upper  end 


jerk  of  the  string.     Next  strike 


the  lath 


through  the 
the  Jath  to 

1  uow  with 
the  result? 

liey  vibrate 

are  inter- 
in  a  com- 
le  time. 
►f  oscilla- 
im.  For 
vliich  the 


om  the 


md  Uie 
1  a  chii) 
ihe  latJi 
le  time 

Strike 
aer  end 

at  the 
lie  lath 


APPLICATIONS   OF  THE  PENDULUM.  12o 

rfrnttMtn '"'■"?  ''^''''  ^''^  '^'^'^•^^  *^«^«  "«  lower  extremity  It 

;:tLrrrh?.!^:i^r;r^^ 

of  motion.     The  base-ball  player  soon  learns  at  what  point  on 
ns  bat  he  can  deal  the  most  effective  blow  U>  the  ball   and  Z 
the  same  time  feel  the  least  tingle  in  his  hands. 

TllTnJT^.r^^  applications  of  the  pendulum. - 
The    orce  that  keeps  a  pendulum  vibrating  is  gravity      Were 
.t  not  for  frietion  and  resistance  of  the  aW,  a  pendufum,lc 
set  n.  motion,  would  never  cease  vibrating.     Since  the  fore 

of  vibration  of  a  given  pendulum  must  be  determined  bv  the 
intensity  of  this  force.     Hence  it  is  apparent,  that  i    the'ra 
of  vibra  ion  IS  known,  the  intensity  of  the  force  of  gravity  mav 
be  calculated.     It  is  found  by  experiment  that  the  time  ^1 
brauon  vanes  inversely  as  the  square  root  of  the  force  of  gravity 
8o  the  pendulum  becomes  a  most  serviceable  instrument  ffr 
measuring  te  intensity  of  gravity  at  various  altitudes  and  a 
differen   latitudes  on  the  earth's  surface.     (Compare  §  21)      j 
•s  also  the  most  accurate  instrument  for  measuring  time  thai  hns 
been  invented.     Its  value,  as  a  time-measurer, 'depend      p^ 
he  absolute  uniformity  of  the  rate  of  vibration  as  long  as  it 
length  IS  constant,  and  the  length  of  its  arc  very  small.     But  a 
heat  IS  ever   modifying  the  dimensions  of  all  visible  bodes 
various  devices  have  been  called  into  existence  by  whidrheat 
may  be  made  to  correet  automatically  its  own  mischief.     Clol 
that  do  not  have  self-regulating  pendulums  are  fast  in  wint 
and  slow  m  summer.     (How  would  you  regulate  thea  2) 


Is  >\  .9 


nm 

!  ■  fm 

'   :  '"If! 


U  f 


;■  !!■ 


m 

I 


12G 


DYNAnrrcs. 


1       w,  QUESTIONS. 

that  swings  it)  should  a  b  owbS  ""  ;;;?."; '^»;'  ^^'^"'^^  «-^  «-"'.„ 
When  held  in  the  hand  at  one-  extremit^;  ''  ""''"'""^  dimensions 

4-      Which  end  of  a  bat  th.  h  "'""  "'"  '^^'^^^ 

hands?    Why?  ''  "'"  ^^"'''«''  ^'  ''^hter,  should  be  held  in  the 

§  85.    Momentum  Tf  i,        i 

ttat  al;  bodies,  under  tl'.e  acLn  f  '^  ^  '"""'  *'"""'<'  <§  ^9) 
Tbu.,  if  a  ouelpound  i  ouMI  f '""'^'  ""'  "'"esarae  rate 
"■'owed  to  fall  V„  ;e"'  d^H  "  '""'■''°™''  ™-  •""'  ^ 
end  Of  t.,e  second  ^a.  aoiS  v  o  il^ 4?;'";  '"«"  ""  «'■' 
Now,  o„  the  „„e.po„„d  tali  a  force  Those  ll!-  "^^  "^'^■ 
lias  acted  conlinuouslv  daring  1!  '"'eMity  ,s  one  pound 

pound   ball  a  force   whose  ™f  ,1    """""^'  """■'  °"  "«=  '"<- 
continuously  during  one  seco  d      r  '"  "">  P"-""' las  acted 
force  has,  during  tl,e  second  tl     T^"  ""'  "f*'^'^-    Each 
locity,  namely,'from  r    "to's".  feeT        '  '"°'°  """"^^  "'  ^- 
produced  the  same  chanl   of  It      f  ?^<"'»<'  ^  but  has  eacl-. 
each  produced  the  saj  effectT'T'  .'"  "'"'"  """f^.  has 
pounds  u>  be  divided  int  tw"  eoual  S"'  ,""'  '""^  "'  ""> 
you  imagine  these  two  eqna  fori,    '°™^  »' one  pound  ;  can 
effeet  other  than  twice  ,1?,  1     T?""'  '°  "'"  '""""^  ™ 
-me  time?    Evidently  not      X:^""^"  "y  one  of  them  in  the 
quantity  of  motion  inVtwo-pI'dbTd"?":"""'''^  """  '"e 

32*fcetperseco„discxa:«/d  „b,e2i:r*  "  "'""'''^-  <" 
I'avmg  the  same  velocitv     L^in    e  one-pound  body 

ball  to  fall  from  rest  freel'v  dtril,  ^'"'  "^  ""^  one-pound 
the   two  seconds,  is   fo  L    H  "T"'' "' »""c  end  of 

second.  Now,  a  one-po  „d  flt"°  ,"  """"'^  °'  «^i  ''^^t  per 
two  seconds  must  produrinH  'T.e'r':""^^  ""^'"^ 
force  acting  continuously  during  one    econdo    °'  '"'  '™^ 

conclude  that  a  body  of  one  Doundl-r.    "™™  "^  """«' 
•^      ""^  P°"™  ""li  a  velocity  of  64|  feet 


MOMEMTUM. 


127 


ixe?    Why? 
t  of  the  arm 
1  dimensions 

ssion  is  pro- 
5  held  In  the 

^ed  (§  79) 
same  rate. 
»n  ball  be 
ich  at  the 
Br  second. 
)ne  pound 

I  the  two- 
has  acted 
;s.  Each 
?e  of  ve- 
lias  eaci: 
rds,  has 

of  two 
ad ;  can 
seond  an 
B  in  the 
hat  the 
ocitj  of 
id  body 
3-pound 

end  of 

'eet  per 

during 

s  same 

3  must 

II  feet 


per  second  has  exactly  double  the  quantity  of  motion  possessed 
bya  one-pound  body  with  a  velocity  of  32^  feet  per  second. 
To  that  which  we  have  called  quantity  of  motion  tlie  name 
momentum  has  been  given.  • 

It  will   be  seen  from  the  foregoing  that  the  momentum  of  a 

Sti J"'n         f^  "  ''''  """  "'  '^^  ^«^'^'  ^->  -•«-  varies 
d  r  ct,,.as  the  velocity  of  the  body.     Hence  a  proper  measure 

of  the  momentum  of  a  body  is  the  product  of  the  measure  of 

Its  mass  mto  the  measure  of  its  velocity.    We  may  also  say  that 

a  uniform  force  actin,  on  a  lody  produces  a  ckanye  of  .Leu- 

tu.x   imts  own  direction  proportional  to  the   intensity    of  the 

themselves,  the  heavier  weight  will,  of  course,  fall,  and  the  light  r^le 

DuLv     Tf  H  !.  "''''''^ ''  ^-^  ^*'^'  b'-'^i'l^^  the  cord  and  the 

pulley.  If  hese  latter  are  very  light  their  motion  may  be  ne-^lLed 
Now  you  already  know  that  a  mass  of  32^  lbs.  if  initially  at  r^  t  Ina 
left  to  the  ac  ion  of  its  own  weight,  that  is.  if  left  to  the  action  of  a 
force  whose  intensity  is  32^  lbs.,  for  one  second,  wi     in  t  a   t^>^e 

T:L^zt:r\ '' '''-  'r  ^°'  ^^^-^^^^  ^^  th^endonirer : 

a  velocity  of  32^  feet  per  second.    Through  what  distance,  therefore 
do  you  expect  the  weights  in  the  experiment  to  move  in  ;ne  second 
and  what  velocity  do  you  expect  them  to  have  at  the  end  of  the  sec- 
ond ?  Compare  the  result  of  your  reasoning  with  that  of  the  expe  ime  t 
Allow,    he  same  weights  to  move  during  two  seconds,  three  secZs 

:;s.'r:;;treSt  -*^*^--^-  ^^^-^^  -e  expenmentr;;; 

The  second  law  of  motion  (§  69)  may  now  be  extended  so  as 

!rr    \j  i^'"''''-^"'''  '*«^  ^^«  ^«^«  effect  in  producing  motion, 
whether  the  body  on  which  it  acts  is  in  motion  or  at  rest ;  whether 

!J'  T^Z^''  ''y  '^^'f^''^  ^'ione,  or  by  others  at  the  same  time, 
and  that  effect  is  to  produce  in  its  own  direction  a  change  of 
rnomentum  proportional  to  the  intensity  of  the  force  andpropor- 
tional  to  the  time  during  which  it  continuously  acts. 


t 


If 

•'■I 


m 

M 

I 


II 


128 


DYNAAUCS. 


ill' 


Kl        .: 


ii 

iml 


QUESTIONS  AND  PROBLEMS. 

1.  Compare  the  momenta  of  a  car  \vpi.r},i„„  m  * 

per  minute,  and  a  lump  of  ice  wrigl  nj^ewt    at  t^""'  ^7'"^  ''  '^ 
second  of  its  fall.  "'^•fe'»»fe  5  cwt.,  at  the  end  of  the  third 

2.  Why  are  pile-drivers  made  heavv?     VVl.v  .„!„    w 

4.  A  body  has  a  certain  momentum  after  fallinfr  ti,r»,.  i 

XIV.     THIRD   LAW  OF   MOTION. 

§  86.    Third  law  of  motion        t*  i,„    i 
fhnf  «,^*-  .       "^°"o°-  —  It  lias  been  shown  f S  67\ 

that  motion  cannot  originate  in  a  sindo  borlv   hnf      •       V^ 

ever  „„o  body  .-eoeivos  ,„„tio„,  anothe,-  body  always  pa  Jwth 
mofon,  or  ,3  set  in  motion  in  an  opposite  direction     tlTat  J 

bodies  oppositely  affected. 

Experiment.     Float   two   bloclcs   of  wr.r..i    ^f 
water,  connecting  thorn  bva  shoflL      Z      \        ""*'''"^'  ™*««««  «« 
end  the  band  wuf    et ^oth  in  l^  h      T'""'  ^^"^^    ^^«*  ^'«  '''-  blocks, 
the  greater  ve7ocitr  '  '"'  '^'  ^™^"^^  ^^«^^  ^-"  ^^^ve 

othtrd\'f\\Ssr£t/anrh*^^  ^""^  ^*  °"^  ^•^^  "^  ^  -P«'  ^'^^ 
as  the  first  man  L  a  IL  ^r.  T""'  ''^^  ^^'"^'^^  ''''^'  ««  '""'^" 
towards  each  otL  ;  L'  in  ^nlfsH^       .T'"  ''^*'  "'^^^^  ^'" '"-« 

.ov  t  ,,  ^;  t  Lrtt  sre^r  ;r^r '  -^^ 
wi^::rct::nr^--;^:-- 

f erent  velocities,  yet  with  equal  momenta.  '       '       ^"  ''''''  '^'^- 

usu.11^   distxagmshed  by  the  tenn«  action  and   region.     We 


.  -^v 


THIRD   LAW    OB'   MOTION. 


129 


return  to 


^'i"ff  10  ft 
tho  tliinl 

It  hi^'hts? 

liavc  tho 

ic  rate  of 

a  certain 
3  its  nio- 


a  (§  67) 
les  from 

can  lift 
ect,  bnt 

When- 
rts  with 
-t  is,  in 
'■ast  two 


Lsses  on 

blocks, 

ill  have 

)pe,  the 
IS  much 
11  move 
Jat  will 

s  boats 
th  dif. 

Bd  are 
We 


measure  these  by  their  momenta.  As  every  force  is  either  a 
l)iish  or  Ji  pull  (§  12),  and  produces  equal  momenta  in  two 
bodies  in  opposite  directions,  hence,  the 

TiiiUD  Law  of  Motion  :   To  every  action  there  is  an  equal 
and  opposite  reaction. 

The  application  of  this  law  is  not  always  obvious.  Thus,  the 
apple  falls  to  the  ground  in  consequence  of  the  mutual  attrac- 
tion between  the  api)le  and  the  earth.  The  earth  does  not 
appear  to  fall  toward  the  apple.  But,  allowing  that  their  mo- 
menta are  equal,  we  are  not  surprised  that  the  motion  of  the 
earth  is  imperceptible,  when  we  reflect  that  the  velocity  of  the 
earth  must  be  the  same  fraction  of  the  velocity  of  the  apple  as 
tlie  mass  of  the  apple  is  of  the  mass  of  the  earth.     (§  85.) 

QUESTIONS. 

1.  The  velocity  nf  the  rebound  or  "kick"  of  a  gun  is  slight  when 
compared  with  tlio  velocity  of  the  ball.     Why? 

2.  Ill  rowing  a  boat,  what  are  the  opposite  results  of  the  stress 
between  the  oar  and  the  water? 

3.  Point  out  the  results  of  the  action  and  reaction  that  occur  when 
a  person  leaps  from  the  ground. 

Fig.M. 


4.  If  there  were  no  ground  or  other  object  beneath  him,  and  he 
were  motionless  in  space,  couid  he  put  himself  in  motion?    Why? 

6.  A  boy,  running,  strikes  his  head  against  another  boy's  head. 
Which  is  hurt?    Why? 

6.  Suspend  two  balls  of  soft  putty  of  equal  weight,  A  and  B  (Fig. 
94).    Draw  A  one  side,  and  let  it  fall  so  as  to  strike  B.    Both  balls 


!l 


ii^^ 


ll- 


1 


130 


DYNAMICS. 


I 


Show  .,««,,,,,„,  ,;-rjrrrsr:/r^^^^^^^ 

veloclt;-,  While  A  Is  brought  to  rest     Show  .STr  """"  •*''  °*°'" 
tent  with  the  third  law  of  moMon  *"  '''""  ''  '°"»'»- 

t«  E,  E  to'^F.  .ri'lins  .otr.","""  v".'  l"""""^ comnunleate, It 
With  C's  original  veloeUv    Trf^I  fh       ,  ^"^  '°  <'°"""™'<:«te  It.  moves 

«.  whaf  woai.  Soh  Sx  r„rTrr  z:^""^ 
ri'rss:::rt,tr^--^^^^^^^^ 

o^e  the  ha.  e.erts7s  tr.tVtrS:ih:  L,„^roJTf 
JRg^M,  would  be  necessary  to  project  C  toe    WTien 

an  das«c  body  strikes  another  fixed  elastic 
oody,  It  rebounds  with  its  original  force. 
Experiment  2.  Lay  a  marble  slab  A  fFic 

tlTn  *  "^^^^^  '"'^  '°"  ""  *^«''J'  ball  in  the 
line  DC,  perpendicular  to  the  surface  of  the 
slab;  the  ball  rebounds  in  the  same  line  to  D. 
f.    n  ^^^"  *°  "''  "°*^^C;  it  rebounds  in 

path  ...e,  with  the  s.™e  perpenaiclar:',:  fZl^^rofTZl' 

It  .s  found  by  raeosuremcnt  that  Uiese  aneles  arc  ^„,„1  wl,.n 

tt.  two  ood,„.  are  perfectly  clastic.    This  equality  is  'expressed 

by  the  Law  o.  Replkction  :  When  the  strik^g  My  „„dTS 


Work. 


131 


;d  with  A's 

es  B,  com- 

r  when  it 

nd  let  fall 
■  collision, 
ion. 

ills,  which 
's  original 
is  consis- 

ke  D.    D 

inicates  it 
It,  moves 
■orghout. 


:Flg.  94) 
'^able,  C's 
covering 
t  in  this 
of  D  as 
y.  When 
d  elastic 
e. 

'  A  (Fig. 
11  In  the 
3  of  the 
ne  to  D. 
unds  in 
its  Ibr- 
ruck,  is 
creating 
flection. 

I  when 
>res8ed 
lebody 

'•  to  the 


XV.    WORK  AND    ENERGY. 

§  88.  Work.-  We  have  learned  (§  43)  that  a  force  may  pro- 
duce either  motion  or  pressure  (or  tension),  or  it  may  produce 
both  eflfcLs  at  the  same  time  and  in  the  same  body.  But  a  force  does 
work,  in  the  sense  i'  vhich  this  term  is  used  in  science,  only  when  it 
produces  motion.  A  irson  may  support  a  weight  for  a  time  and 
become  weary  from  txic  continuous  application  of  force  to  prevent  the 
weight  from  falling,  or,  in  other  words,  to  prevent  the  force  of  gravity 
from  doing  work,  but  he  accomplishes  no  work,  because  he  effects  no 
change,  i.e.,  causes  no  motion.  The  body  that  is  moved  is  said  to  have 
work  done  upon  it;  and  the  body  that  moves  another  body  is  said  to  do 
work  upon  the  latter.  When  the  heavy  weight  of  a  pile-driver  is 
raised,  work  is  done  upon  it;  when  it  descends  and  drives  the  pile 
into  the  earth,  work  is  done  upon  the  pile,  and  the  pile  in  turn  does 
work  upon  the  matter  in  its  path. 

Whenever  a  force  causes  motion,  it  does  work.  A  force  may  act  for  an 
indefinite  time  without  doing  any  work;  but  whejiever  a  force  acts 
through  space,  work  is  done.  Force  and  space  (or  distance)  are  essen- 
tial  elements  of  work,  and  are  naturally  the  quantities  employed  in 
estmiating  work.  A  given  force  acting  through  a  space  of  one  meter 
will  do  a  certain  amount  of  work ;  it  is  evident  that  the  same  force 
acting  through  a  space  of  two  meters  will  do  twice  as  much  work. 
Hence  th*.  general  formula, 

W  =  FS,  (1) 

in  which  W  represents  the  work  done,  F  the  force  employed,  and  S 
the  space  through,  which  the  for^^e  acts. 

In  case  a  force  encounters  resistance,  the  magnitude  of  the  force 
necessary  to  produce  motion  depends  upon  the  amount  of  resistance. 
Indeed,  in  cases  in  which  the  body  having  been  moved  through  a 
given  space  comes  to  rest  in  consequence  of  resistance,  the  entire 
work  done  upon  the  body  Is  often  more  conveniently  determined  by 
mtdtiplying  the  resistance  by  the  space  through  which  it  is  overcome,  and 
our  formula  becomes  by  substitution  of  resistance,  R,  for  the  force 
which  overcomes  It, 

W=RS.  (2) 

Tor  examrV,  a  ball  is  shot  vertically  upward  from  a  rifle  in  a  vacuum; 
the  work  done  upon  the  ball  iiuiy  be  estimated  by  multiplying  the 
average  force  (difficult  to  ascertain)  exerted  upon  it  by  the  space 
through  which  the  force  acts  (a  little  greater  than  the  length  of  the 
barrel),  or  by  multiplying  the  resistance  offered  by  gravity,  i.e,,  its 
weight  (easily  ascertained)  by  the  distance  the  ball  ascends.    Also,  la 


I 


I  J 


132 


t)YNAMICSl. 


w 


M      1 


It! 


li^ 


gravlw  b,  the  first  foZ„     „»„  1.  Is"™    T  <'"  ""^  "»»  "J- 
that  part  of  the  work  don/l„  „     ?    !  ^""■'"'  '°  estimate  onir 

«lven  .n  SHwniTfot:  I'T^flTr"""'  '"=  '°™""^' 

p4e?wh«tsta,:';^tta'::„t'o/tT  ?""-  "■' """  ™- 

§  96  ivlll  be  defined  the  nnf,  ^f        the  elements  of  work.     (I„ 

employed  asafSrof  ,™'krT  f  .rT'T"  """°  ""=  '»-'"» 
French  Is  the  work  done  In  raSnl  nV"  f  "">*  """P'"'  "y  the 
It  Is  eaued  a  mo,ra:V::,!^^SZ:^;i%"^r  'l'^'  <>'  '"• 
work  Is  that  done  In  raisino-  oL  „„    T  ''        "  >^"gh»h  unit  of 

;>™nd.  ThckilogZm  eflsahont °rw°°  "'°''  ""  "  «'"  "/»»'■ 
the  foot.po„„d.  Now  Shu  e  tl^e  w  ?  'r''  "'=™"'«'J.  '-233)  times 
l'",  the  work  Of  r.,,„;J"  r,  ImZH,  '  ZJ"  ?:1"«  "  ■■"  '"«"  '» 
the  wo.  done  ,„  ralslnj  ,.  |.„  hSl  Tn^r 're'rl^ahrrSr 

ButX":,t7rermrrtrertr^v;'"°'™*-"'^'>- 

any  other  direction  is  just  the  sal  «!  T,?  P''^^"^'""^  motion  in 

easy,  in  all  cases  in  whLuhetre,ellV""f  ''''''''-'  '^  '« 
and  spa.e)  are  known,  to  find  t  eo  h a  '  in  J"[\^^'"'  '^^'^^^°«« 
weight  vevtically.    By  thus  securinrn  '^'''''  ^^"^  '"^  ™'«ing  a 

nlentofwork^v^LreaSe  trc^nnare  r""'"  '''"'''''  ^^  "'^'^^"re. 
other.  For  instance,  lot  s  compare  h  7  ?T'  ''  ^^"^'^  ^^'"^  -»y 
through  a  stick  of  vv'ood.  w,rr:  .11''^  ''  T  "^"  '"  ^'^^^'"^ 
resistance  of  12^  with  that  done  by  a Tui lun  V  ."'""'* ""  "^''^•'^S^ 
depth  of  2cm  against  an  average  ro,i«f         f"''''*''"^'*^^'*"'^  to  a 

10'"  against  12^  resistance"  eo.l  I     '^  '    ''''•    ''"^■'"»"  '  ««- 
doing  120^.™  Of  work;  a  hul,et:r  „t  L^aT n^'ir  ?"  '''''  "^ 
as  much  work  as  Is  required  to  raise  2004:",.,''^   T^'*^^ 
of  vvork.     120  -^  4  -  qn  fim^.  ,  '*'»'''  o""  200  x  .02  -  4 Vgn. 

the  bullet.  ''  "'"''^  ''  '""^''  ^-••'^  ^o»o  l,y  the  sawyer  as  by 

§  90.  Rate  of  doing  work  —  Tm    „  .•      .. 

„   ..,  ^oijv  dune,  the  tune  consumed  is  unt  f..i'     •  ~.     " 
sideratiou.     The  work  dn,.P  1»,     i     ,  '''^"  '"*«  con- 


"le  force  are 
there  is  no 
I  body  falls 
his  case  by 
timate  only 
le  formula." 
titiited  for 

tmit  em- 
vork.     (In 

0  force  is 
ed  by  the 
a:ht  of  im, 
ih  unit  of 
ed  a  /oot- 
ids) times 
'"  high  is 

>  same  as 
us  raisiiis"; 

:  weights, 
notion  in 
ion,  it  is 
esistance 
raising  a 
measure- 
vith  any 

1  sawing 
average 
ank  to  a 
g  a  saw 
I'gh,  or 
ice  does 

2  =  4  '"■gni 

r  as  by 

totn! 

o  con- 

1 ,000 

s  it  ID 


POTENTIAL  AND  lONETIC  ENEEGY.  I33 

a  day  or  a  week.     But  in  estimating  the  power  of  any  agent  to 
CO  work,  as  of  a  man,  a  horse,  or  a  steam-engine,  in  other  wo.^f 
t^te  at  which  it  is  capable  of  doing  worf,  it'  is  evidm:; 
time  IS  an  important  element.     The  work  done  by  a  horse,  in 
raismg  a  barrel  of  flour  20  feet  high,  is  about  4000  ft.-lbs 
but  even  a  mouse  could  do  the  same  amount  of  work  in  time' 
Ihe  unit  m  which  rate  of  doing  work  is  usually  expressed  is  a 
horse-power.     Early  tests  showed  tliat  a  very  strong  horse  ma^ 
perform  33,000  ft.-lbs.  of  work  in  one  minute.    lo  1 TJ'. 
power  =  33,000  ft.-lbs.  per  minute  =  550  ft.-lbs.  per  second  1 
nbout  4570^-  per  minute  =  about  76^-  p,,  ,,^  J^^  ^'^^^"^  ~ 

§91.  Energy. -The  energy  of  a  body  is  its  capacity  of 
doing  work,  and  is  measured  by  the  work  it  can  do.  Doma 
work  usually  consists  in  a  U^asjer  of  motion,  or  energy,  from 
the  body  doing  work  to  the  body  on  which  loork  is  done.  Wher- 
ever we  find  matter  in  motion,  whether  in  the  solid,  liquid,  or 
gaseous  state,  we  have  a  certain  amount  of  energy  which  may 
often  be  made  to  do  useful  work.  ^ 

§  92.  Potential  and  kinetic  energy.  _  Place  a  stone, 
weighing  (say)  l()^  on  the  floor  before  30U  ;  it  is  devoid  of 
energy,  powerless  to  do  work.  Now  raise  it,  and  place  it  on  a 
shelf  (say)  2-  high  ;  in  so  doing  you  perform  20''«">  of  work  on 
It.  As  you  look  at  it,  lying  motionless  on  the  shelf,  it  appears 
as  devoid  of  energy  as  when  lying  on  the  floor.  Attach  one  end 
of  a  cord  3"'  long  to  it,  and,  passing  it  over  a  pulley,  wind  2'» 
of  the  stnng  around  the  shaft  connected  with  a  sewing-macliine, 
ooflee-m.ll,  lathe,  or  other  convenient  machine.  Suddenly  with- 
draw the  shelf  from  beneath  the  stone.  It  moves,  it  sets  in 
motion  the  machine,  and  you  may  sew,  gi-ind  coffee,  turn  wood, 

etc.,  with  the  power  triven  to  iho  rpoohino  1—  fi»  -^-.,-- 
'  ••  -  —  .!...!  Nine  i/j  tiU;  atOiiu. 

Surely,  the  work  done  on  the  stone  in  raising  it  wa..  not  lost; 
the  stone  pays  it  back  while  descending.  There  is  a  very  im- 
portant  diflference  between  the  stone  lying  ou  the  floor,  and  the 


II 


iii 
m 

I 


m 


hrNAmcQ, 


see  no  differen*  «*»         /        ^'  motionless,  and  you  can 

at  rest  ,s  not  necessarily  devoid  of  e„e»r  Ttht  «^  ° ,  "^ 
passively  on  the  shelf  there  exists  a  n^^.\  !,         .     ""  '*"'8 

th.t  possessed  by  the  stone  whth  El  ^r^,  T' ■"""  "^ 
great  velocity.  '""°''' """"g 'reely,  has  acquired 

diii::;at:'aX:tTri;:fin '"  ""-^^  -' '"°  '^"^■^ 

K  my  exist  as  oo  J.  L^^,  e7«L    vSb.r"  "  '°  ""r"""- 
c">tion,  or  invisible  a,  in  th.  ^T    ,  '  "^  '"  mechanical 

it  may  exist  in  Lm  ^  molecular  motions  called  heat;  or 

*;'  mrrCcZ  r*'t'/^  •"  *^^  ^'°"'  '^-s  on .:: 

ene.^;  in  the  kZ  it  t     Tw  ""  *"'*''  ("""^'"S)  °'  «<*■«" 

-TmvTioiTtirit™'  *"  '*""  "'•  "^-'"^^  <•- '"'-  - 

gradually  in  the  movLento  S  tht  I  '  *"  ""  *'"^  »»' 
when  we  bend  the  to  "  raTse  .hi  K  """"""»'y-  ^e  store  it 
rai«.  any  body  above^^;  e^L'sur^a^ ""'  ""'*'''"  ""'  ""<> 

do  work,  as  when  mills  a.t  driven  bv  17  "  '■""i"^'"  '" 
water;  but  the  water  i,  fl~,t  j        ■    J         P"""  of  falling 

one^of  thesunfhe  ri^JSlf  2  '''  •'""^"''  ''^  "■° 
a  motive  power  •  but  el„«t,v  ,    •   ^  ^        """"^  "  ^mp'oyed  as 

Which  the'mrc'ul    'o  'CS  Lv^t ""  1™""^'  "' ''°''«''» 
force  appBed  to  tliem.  ^""^'' '"  "o^^iue-ee  of 

We  conclude,  then,  that  a  6oA,  «r..^.^.  , 

«Ae»,  m  w«ue  0/ ,oor*  <fo„e  „«„„  ft'',-: ™. '"*""•«'  e««w 


FORMULA  FOB  ENERGY. 


135 


tUmergy  expended  can  be  at  any  time  recovered  by  the  return 
oj  the  body  to  Hs  original  position,  or  by  the  return  of  its  mole- 
cules to  their  original  positions. 

A^l    Energry  contrasted  with  momentum.  -  Problem. 

A  bullet  weighing  30«  is  shot  with  a  velocity  of  98n.  per  second  from  a 
gun  weighing  4-  requir.  d  the  momentum  anc^  the  fnergy  of  both^ 

kilogram,  the  meter,  and  the  second  as  units,  the  momentum  of  tl,P 
ball  IS  .03X98  =  2.94  units.  If  the  ball  were 'shot  verrairupl^ 
Its  velocity  would  diminish  9.8«  per  second;  so  it  would  iise^=  lo 
seconds    and    therefore,  before  its  energy  is  expended,  to  a"hight 

iion  ,f!  J  ""'^''^  ^^^  "'^  S"°'  ^y  the  third  law  of  mo- 

units     ir*"?    7  "'"f  '"  ^"'^  ''''  «^™«  *«  *h^*  of  the  baU,  2  94 
735  ''  '^°''  ^"^^  ^  '^  =  •'^''"  P^^  «««°"^-     Then 

'^=  9X=  -^^^  '•'^°°^'  the hight  (supposing  the  gun  to  be  raised  verti- 

T:^'^^t:':n:,i:r'''^  =  ^-^  ><  -O^^-  =  •02766»;  and  its  energy 

While,  therefore,  the  momenta  generated  in  the  two  bodies  by  the 

burning  of  the  powder  are  equal,  the  energy  of  the  bullet  is  ilil  =  133 j 

times  that  of  the  gun.     (Why  are  the  effects  produced  by\^h!  bullet 
more  disastrous  than  those  produced  by  th»  recoil  of  the  gun?) 

§  94.  Formula  for  energy.  _  We  can  find,  as  in  the  above 

example,  Uy  what  vertical  hight  a  body  having  a  given  velocity 

would  nse,  and  thus  in  all  cases  determine  its  energy ;  but  a 

ormula  may  be  obtained  which  will  give  the  same  result  with 

less  trouble ;  thus :  ,  ""mm 

Let  E  =  measure  of  energy,  in  foot  pounds. 

''  velocity,  in  feet  per  second. 

"  acceleration  due  to  gravity,  =  324. 

"  hight  to  which  body  would  rise,  in  feet. 

"  weight  of  body,  in  pounds. 

♦*  time  of  rising,  in  seconds. 


"   V  = 

9   = 


i( 


(( 


S  = 

"  w  = 

"   T  = 


(( 


» i'ii 


!lM 


136 


DYNAMICS. 


T  = 


i"* 


or    T''= 


0 
if 


9 


But  K  =  ^v  s 

_  1^  ^'' 


Itis  Pvident  that,  when  the  wehjht  ( W)  of  n  hnrh.  ,.        •        , 

tls  momentum,  as  wc  h-ivo  lo-.m,.!  "^       ''''^^""'^'  ''^^"■'^' 

rn  other  words    thHii    .    7  '  '•^"  ^"•'''"^'•^'■"««^  «<^  *V.  .e/oaVy. 

^.>iciiy  than  its  .o^ear^'rihi:;::^^^^^^ 

to  four  tunes  the  depth  that  it  did  in'the  fonne';        ""  "  "''^'^^'•^^^^ 
moving  with  a  ve'ocitv  of  ion  e.   ,        "^^'<^*"i  etc.     A  bullet 

"ot  twice,  b„t  fortii  ."L!"!;':  z"":  *'"'  "r-"'-""' 


MEASURE  OF  A  FORCE. 


137 


Which  a  hor.se  draws  a  wagon  is  SO-^ ;  that  is,  a  spring  interposed 
be.ween  the  horse  and  tlie  wagon  is  stretclied  just  as  much  as  it 
would  be  by  the  force  of  gravity  acting  on  a  mass  of  50"  hung 
from  the  spring.     But  often  it  is  impossible  to  measure  the 
force  except  by  the  motion  it  produces.     Experience  has  shown 
that  a  useful  ana  accurate  measure  of  a  force  is  the  momentum  it 
produces  or  destroys  in  a  second;  if  the  body  is  already  in  mo- 
tion, we  must  say  the  change  of  momentum  produced  in  a  second 
iov  example,  gravity  we  know  will  impart  in  three  seconds, 
f  %      oL^"^'"^  ^  '"'''  ^^  ^'^^^)  ^''  ^"^^  ^'^^  ^  f^"'  a  velocity 

&  X  6  X  980.  Then,  by  definition  above,  the  measure  of  the 
force  of  gravity  on  the  body  is  62<3^9^  ==  5  ^  980.  When  the 
centimeter,  gram,  and  second  are  taken  as  the  units  of  len-th 
mass  and  time  respectively,  the  system  of  units  of  measurem'eni 
based  on  them  is  called  the  C.G.S.  system,  and  in  it  the  unit 
of  force  IS  called  a  dyne. 

A  dyne  is  that  force  lohich,  acting  for  a  second,  wiU  give  to  a 
gram  of  matter  a  velocity  of  one  centimeter  per  second.  In  the 
example  above  we  have  a  force  of  5  x  980  =  4900  dynes 

The  gravity  unU  of  force  is  the  weight  of  any  unit  of  mass 
e.j7.,  a  gram,  kilogiam,  pound,  or  ton.  In  distinction  from 
gravity  units,  the  C.G.S.  units  are  called  absolute  units.  Gravity 
muts  are  easily  changed  to  absolute  units;  thus  in  Ontario  the 
foice  of  gravity  acting  upon  P  of  matter  .free  to  fall  will 
give  It  an  acceleration  of  velocity  of  980-  per  second  per  sec- 

:bi^  J;:r  [ti:  ^'^^  ^^''''^^' ''-  ^^^^^^^  -^^  ^«  ^^-^  ^^  ^^^ 

Let  M  =  measure  of  mass  of  body,  in  grams. 


(( 


(( 


W 
F 


9  = 


u 


weight  of  body,  in  dynes, 
attraction  between  earth   and  bodv,  in 
dynes. 

acceleration  due  to  gravity,  in  absolute 

units  =  980. 
W  ==  F  =  M  ^. 


'    Ml 


138 


DYNAMICS. 


11 


The  equation  is  a  general  one  ;  tliat  is,  wlienever  any  two  of  the 
three  quantities  specified  are  known,  the  third  mav  be  coi^put^ 

con  i^pl  r'  "^^'J'''^  ^^^^'  ^"^^'^y'  ^"*  ^^'"^t  resistances 
considered  as  constant,  such  as  the  forces  shown  in  cohesion 

elasticity,  etc,  the  equation  will  still  be  true,  only  a  should  b^ 
replaced  by  some  other  letter,  as  a.  J  y     "uia  oe 

Now  let  us  learn  what  is  the 

J.^ ,  ^T'^^f  *^«  ^fi'^^*  <>^  a  force.  -  One  measure  we 
know  already, -the  product  of  the  force  into  the  distance 
through  which  It  acts;  that  is,  the  work  done,  or  the  enerau 
imparted  to  the  body  moved,  is  a  wmmre  of  the  effect  of  afoZ 
If  the  fon^e  is  measured  in  dynes,  and  the  distance  in  cenfa- 
meters,  the  work  done  will  be  expressed  in  a  C.G.S.  unit  called 
an  erg     An  erg  is  the  work  done  or  energy  imparted  by  a  force 
of  one  dyne  working  through  a  distance  of  one  centimeter.    Be- 
sides  the  erg  we  have  the  common  gravitation  units,  the  kilo- 
grammeter,  and  foot-pound ;  that  is,  we  have  another  measure  lust 

Tu^tT/  ''7  '"""^  '^^^ ''  "»^—  ^-  commor;Li,gr 

just  as,  for  mstance,  we  may  express  lengtJis  in  inches,  meters, 
01  miles ;  masses,  m  grains  or  pounds,  ct«. 

Experiment  1.  Suspend  by  a  long  cord  a  heaw  bodv      ink«,«.^ 

SL' ;ro^-i  ^-  --  -^^^o^^^i^ic  z 

(B^)T7tZ^\  ^r'l"^  ^^  *  '*'^°«  ^"^  *°°8  *  «*°°«  ^hose  mass  is 
(say)  5k.    Attach  to  the  stone  a  No.  36  cotton  thread-  thU  win  «.,.. 

port  about  1.^.    Pun  the  baU  slowly  to  one  sideTwhenT^s  boen 

drawn  about  20em  from  its  place  of  rest,  the  thrsad  wlU  brel^L   , " 

ban  w,U  swing  back  to  the  other  side  like  a  pendulum^  an^t>  when 

passes  through  Its  lowest  point  It  has  a  definite  momentum 

in/th^/i  ""Z  ^'^T  ""^  '^'^^^'  *°^  P""  ™°^«  a°d  more  quickly,  bmk- 

Dg  the  thread  each  time;  the  motion  produced  Is  less  and   !;«     As 

the  strinc  Is  strftjffhfon^H  ♦!,«  i^-ii!  —  «-  •  -  ^^ 

ty,^  „       "  \^' — ° '"         P'^"  ""  "  increases  I'rom  zero  to  1^-  «r» 

nir^Z^ZTV"^'  V^r  *'^  ''"^^'^  *"  gravitation  units! 
nearly  or  exactly  ^k.    Here,  as  before,  with  the  same  force  the  manu,^ 

tumproduced  varies  as  the  time  during  u,hich  the/orve  ^  ^'^ 


MEASURE  OF  THE  EFFECT  OF  A  FORCE.  139 

But  If  we  use  stronger  and  stronger  threads,  we  may  pull  more  and 
more  quickly  than  at  first,  ani  yet  give  to  the  ball  init  the  TZ  2 

7oZV"  ^\'"'V''^'  *«•  '^'  ^ff'<^^  of  a  greater  force  acting  for  a 
shorter  time  is  to  produce  the  same  momentum. 

So  far  then  as  our  experiments  go,  they  teach  that  the  prodnct 
of  a  force  into  the  time  it  acts,  or  the  momentum  produced,  is  a 
ir^asure  of  the  effect  of  a  force.  We  may  draw  the  same  conclu- 
sK>n  from  our  last  equation,  F  =  M^ :  multiply  both  sides  by  T, 
the  time  during  which  the  force  acts,  and  we  have  FT  =  M«T 
=  M  V  =  Momentum.  If  T  equals  one  second,  we  see  that 
the  momentum  of  a  moving  body  is  the  measure  of  the  force 
that  would  in  one  second  give  it  this  motion.  It  is  evident 
that  if  motion  is  to  be  produced  by  a  force  acting  for  a  very 
short  time,  the  force  must  be  enoi-mous. 

We  have,  then,  two  measures  of  the  effect  of  a  force,  —mo- 
mentum^nd  energy.    The  first  is  found  by  multiplying  the  force 
by  the  time  it  acts ;  the  second,  by  multiplying  the  force  by  the 
spa^e  through  which  it  acts.    The  latter  can  also  be  found  by 
multiplying  the  momentum  by  one-half  the  velocity.    One  is 
M  V ;  the  other  is  ^  M  V^   Wliich  is  the  con-ect  measure  ?   Both 
are  correct;  so  the  question  now  is,  Which  is  the  more  useftil? 
Experience  shows  that  momentum  is  a  useful  measure  only  in 
cases  where  the  force  acts  all  the  time  in  the  line  of  motion,  aa 
m  falling  bodies,  or  where  it  acts  for  so  short  a  time  that  the 
body  does  not  sensibly  change  its  position  during  the  action,  as 
m  the  cases  of  a  blow,  a  jerk,  coUision  between  balls,  etc. 
Kxperience  further  shows  that  energy  in  all  cases  gives  a  useftil 
nieasure. 

§  97.  Summary  of  mechanical  units,  and  formulas  for 
their  determination.'-Thc  following  tables  show  the  quanti- 
ties measured,  the  unit  of  each  in  the  C.^S  s-«t-m  -nd  *he 
formulas  for  the  determination  of  the  derived  quantities  "1  " 

•dT.n«KJ.tudent  cannot  ftll  to  be  greatly  pwflted  by  iu„«to?^^        *"'  """ 


S  ! 


ll  V- 
i  i 


i, 


ll' 
w 


%  ■     M 
ll 


"  DYNAMICS. 

FUNDAMKNTAL  QUANTITIES  AND  UNITa 

Lengtii  (L  or  S) icm. 

Mass  (M) 28 

T*™«cT) ;:;:;:  1,,^ 

PERIVED  QUANTITIES.  UMTS,  AND  FORMULAS 
Velocity  (V^)  -  rate  of  motion  ;  unit,  ic™  per  sec. ;  in  ...iform  n^otlon. 

'  T'  (1) 

Acceleration  (A)  =  rate  of  change  in  velocity;  unit,  an  increase  of 
velocity  in  1  sec.  of  ic.  per  sec. ;  body  starting  from  rest  under 
constant  force,  A  =r  — . 

^'"   pj'il  '''''^'  °^  "^^^'^  ^°^^'^  (I')'    ""^it.   1  erg  per  sec.; 

Momentum;  unit,  U  moving  with  a  velocity  of  i™  per  sec    or^that 

produced  hy  1  dyne  in  1  sec. ;  Momentum  =  M  V 
From  (2)  amU3)  we  have  the  very  useful  equations,  F  =  MJ  and 

~   M~'  (6)  and  (7) 

A  body,  mass  M,  acted  upon  by  the  force  F.  starting  fVom  rest  will 
acquire  in  time^T  a  velocity  V  =  O^ .    The  acceleration,  which- 
from  (3)  IS  =-  -,  Is  a  constant  quantity,  and  the  whole  space 

veTcl"'Thrl'fr'"''*\*^'  "'"'^  '^  '"•"^'^''^^  ^y'^<^  '"^"'^ 
^eloc^   The  latter^ ^s^one-half  the  final  velocity;  hence,  mean 

-  2  jj.  and  S  =  ~  (an  equation  of  great  importance).  (8) 
To  find  an  expression  for  the  energy  of  a  moving  body  combine  (4)  and 
C3):W  =  y?,butFT.My,...E  =  &  '  [.^ 

1  «    -  98,000,000  ergs;  1  foot-pound  ==  13,650,000  ergs 
1  horse-power  =  447,000,000,000  ergs  per  min. 

§  98.  Transformation  of  energy.  _  In  ti.e  operation  of 
raismg  the  stone  (§  92),kiuctic  energy  is  UaasformedVnto  poten- 


PHYSICS    DEFINED. 


141 


tial  energy.  During  its  descent  it  is  re-transformed  into  kinetic 
energy.  If,  instead  of  boing  attaeiied  to  maciiinery,  and  tl.ereby 
made  to  do  work,  tlie  stone  is  allowed  to  fall  freely-,  it  acquires 
great  velocity.  On  striking  the  ground,  its  motion  as  a  body 
suddenly  ceases,  but  its  molecules  liave  their  quivering  motions 
accelerated.  Mechanical  motion  is,  thereby,  transfonned  into 
heat.  We  shall  often  have  occasion  to  examine  the  transforma- 
tions of  energy,  as  into  electric  energy,  heat,  etc.,  but  never 
of  momentum.  We  shall  study  Joule's  equivalent  (§  14G), 
expressing  the  relation  between  the  unit  of  energy,  or  work, 
and  the  unit  of  heat ;  but  it  is  certain  that  there  is  uo  relation 
between  the  latter  and  the  unit  of  momentum. 

§  99.  Physics  defined.  —  All  physical  phenomena  consist , 
either  alone  in  transferencis  of  energy  from  one  portion  of 
matter  to  another,  or  in  both  transferences  and  transformations 
of  energy.  Transformations  may  be  from  one  condition  of 
energy  to  another,  as  from  kinetic  to  potential ;  or  from  one 
phase  of  kinetic  energy  to  another,  as  from  mechanical  motion 
to  heat ;  or  both  may  occur,  as  when  the  falling  stone  does 
work,  a  part  of  its  energy  being  expended  in  producing  mechan- 
ical motion,  and  a  part  being  transfoimed  into  heat,  occasioned 
by  friction  of  the  moving  parts. 

Physics  is  that  branch  of  natural  science  which  treats  of  trans- 
ferences  and  transformations  of  energy.  It  does  not,  however, 
in  its  usual  limitation,  include  a  group  of  phenomena  which  occur 
outside  the  earth,  and  also  a  group  whose  essential  character- 
istic is  an  alteration  in  the  nature  of  the  material  considered. 
Tlie  study  of  the  former  group  is  the  object  of  Astronomy;  of 
the  latter,  that  of  Chemistry. 

QUESTIONS  AND   PROBLEMS. 

1.  Does  the  energy  expeuded  in  raising  the  stones  to  their  places  in 
the  Egyptian  pyramids  still  survive? 

2.  What  kind  of  energy  is  that  contained  in  gunpowder? 

8.   What  transformation  of  energy  takes  place  in  b     ling  coal? 

4.  When  steam  works  by  expansion,  its  temperature  i^ioduced.  Why? 


f  iH 


\4 


h} 


142 


DYNAMICS. 


.'      I:  I 

A.  li  I 


•■  How  much  work  fs  done  uer  Imnr  ip  ook  . 

9-  «.)  What  enorsy  m„,l  l,e  h  marM  ,„  I  ^"""'  *"  P"  °"»"««' 
m»y  rise  4  sew,,,*?  (ft,  iWriZvll^,  "^^  "''''«'''°« '"«•'«  " 
l.=parted  to  the  same  bout  t  mu  T/  /"  '""'"'  '='""■»  """«  bo 

«t  .he  i,„w„„  u,e  body  I"  th'rowl  "  «'"°  "" ""'  '^'  1°«»"<">. 

H,.i»mr„;t::r:h:rra'e°ep'  ^^  "*-  -■*  ^»'."  a 

Of  L";:™!™""'  "°""'  "■"  -""=  ^-"^  -«-  "  •'  had  .  velocity 

H  "err:::  r^fe  t:tnr,;.;r' — --» ™-.y  „„„« 

the'Ugyr""  ■■'"  "■""«"  «'-"■.  """would  become  or.  p.^t  o, 

.nufa,  'el„'ct:*"2;":.tl"feclV'  t" ""  T'"°"^  """''"'  """  « 
J3.   What  become.,  of-itVrS  du"" .^  ^ trtT  ""  '" 

a  velocf.;^ofTC  llZT^TX^  """'  """""'"^  '»'■  »°1  "avios 

-,  ..v,„,  a  iity  o^r^rirrTft^^- ra 
..itpi;t;zr.rar:-;-'-^^^^^^^^ 

"•  Expla „„  a  e|,iy  „j  '  iin  ,oi  ? 

welshing  jsol.  "  ""'  ""  ^^  <^«»  draw  a  carriage 

■stand,  a.  ^J»  '"  af  rrt'  h"  """"  ""'  '""■-  '»  «^-h'" 

the  rate  l„  h,„.„„-p,,„,rr    (See  5  »  "  ''°"'"'^'    »  E^f"''' 

aci.:,;tr;;r™^*:;^:a:'::;„;?r  »'.'■"-»  p-"  >  p.oww,th 

they  travel  at  the  mte  of  3"  per  hZ'  ""'""'  '°  '"''"'  '""  P'""  " 
h„„",  '"'"  '""-Pow"  '■>.■■.  engine  will  raise  1,350,000.  6.  ,„  an 
^^^»0.  How  lon,  will  It  .ate  a  3  horse-power  engine  .0  raise  10  tons  « 

S»..  How  lona  would  I,  "a?e  ,  ~r?  TT*'°°  ""  '°  ''°  "o"' 
orworj  a  man  can  do  In",  day  bernraTo^  ^toXr"'  "^  "■"°"°' 


USE  OF  MACHINES. 


143 


Fig.  96. 


A 

f  

§100,     Usesof  machines.  — Experiment  1.     Obtain  from  a 
hardware  store  two  or  three  pulleys,  and  arran-e  apparatus  as  In  Fi- 
96.    The  dynamometers  a  and  h   read  4  lbs.  each,  showing  that  the 
povver  (P)  employed  to  support  each  weight  (W)  of  8  lbs.  is  just  one- 
half  of  the  weight.'    If  the  power  applied  in  each  instance  is  slightly 
increased,  the  weights  - , .-   ise.    liaise  each  of  the  weights  and  meas- 
ure the  distances  trav;iv«»ed  I'c 
si)ectively  byW  and  ;  in  ,;;i,oh. 
Through  whaidista  -ce  Must 
P  move  that  W  may  be  raided 
one  foot.     What  amoiv     of 
work  is  done  in  raising  8  lbs. 
one  foot?  How  does  this  worlj 
compare  witli  the  work  done 
at  P?    Is  any  work  saved  by 
raising  the  weight  by  means 
of  the  pulley  instead  of  lifting 
it  directly  ?    Is  a  force  of  less 
intensity  required  when  the 
pulley  is  used?      Since  the 
string  is    light,  and    passes 
round  freely  revolving   pul- 
leys, its  tension  may  be  sup- 
posed to  be  the  same  through- 
out its  length.    What  is  Its 
tension?    Since  the  8  lbs.  is 
supported    by    two   parallel 
portions  of  the  string,  Miiat 
must  the  tension  be?     What 
iloes  the  dynamometer  P  show  the  tension  to  he? 

r.„  cvciy  1  11.  tliat    W   moves        Xnw    •>  (fi  ^    v    m  /n       1 

32  foot-pounds  of  work  done  by  P.     Lx  4  m    '  i  8  1^  I       'V  7 
ponufls  nf  ..roH' -"-.j.-    ,.        «-    ■---        '"'"*'-"'>'  X  «>  (lus.)  =i{-' loot. 

o.  app,.n.  the  ^^-u:^^::^::!^'^:,  r  zr 

« A  email  allowance  muHt  be  n.a  I.  fo,-  ,.,o  weight  of  .ho  movable  pulley,. 


'1  A 


\ 

iP 

^ — , 

.. 

sib,   W 


p; 


144 


LAW  OF  MACHINES. 


i 


•'y  the  use  of  apparatus?     We  found  tbnt  w 

and,  consequently,  with  twice  the  y7olytL7v  '"'''I  ''''''  ^'  ^'' 

It  thus  appears  that,  if  it  should  be  SI     ,!  ""'"'■ 
greater  velocity  than  it  Is  poss  ble  or   '  ™°^'  * '''''^'''  ^'"' 

n>oveJtn.aybeacco„,plisLlt?roth  h  T''"*  '"'  *^^  P^^^'^-"  *« 
applying  to  it  a  power  pro  on  o,,nf  "'''''*"''"  °'  *  ™^^1"»«.  by 
apparatus  is  one  of  ZvcoT  ^  ^''''''''  "'^"  '^^  ^veight.    This 

advantages  derived  fro.  th:te IV^Ichn r/s^:.  -^'"^  ^'  *''^  ™^"^ 
««^/^   ^'"^  """-^  '""''*  '"  ^^  -"•'^"'-^  «  /«ra.  resist 

the  forces  of  wZ       'f' "'^  strength  of  animals, 

t-iastt.:or;;L;:s.:^^'-  ^---« 

The  ratio  of  the  weight  to  the  power  In  any  syste.n 
of  pulleys  may  be  easily  calcuLed  , " 

makinguseofthefact  that  the  tension 
of  the  same  string  is  the  same  through- 
out ^ts  length  so  long  as  it  passes  romul 
T1.0  weight  is.  Of  course,  the  r  s  S'ofto'f  ■"•'"'"'""^"P""^^'' 
'■'""  <'-^  power  is  the  tension  or  the  Isl-u't  if  h'T"'?  ^"PP°r*'»g  't, 
's  supported.     What  Is  the  ratio  of  ,  e  lei'^J  ^' "  ^"■^*-^•^^  ^vhich  it 

wcignr,  to  the  power  In  Fi;;.  !>;? 

§101.    Lawof  Machines.  — Let  Pl»ti,„„„ 

timo,  W  the  weight  moved  or  extern!  eL'e7„  '"  "  '''™" 
"'  M.e  .„.canee  through  which  it  i  lov  , T 11^™°""''. ""'' 
the.  the  ,„eeh.,.|«„  w„rk  .ap„,ie„  to  the  :  L  ,  vZ  T"  '' 
k..ogran,„,eters  or  f„„t-p„,„„„) ,  .,„„  „,„  ,„„,,     i    .^^^  r,;;" 


LAW   OF   MACHINES. 


145 


tTj:J;Z'''^!  -ad.ines    without  exception,  the  follow- 

No  machine,  therefore,  creates  or  increases  energy.     No  ma 
elnne  gives  back  more  energy  than  is  spent  upon  ft      P  can  be 
made  as  small  as  we  please  by  taking,    c.,eat  e  oth     i^  fh 
ease  we  see  that  -P^'o^omo/a.^o«;:/.;'Itr  Z    'rfl 
or  velocity  is  lost.     On  the  other  hanrl   tr^^'"'"^:  '.'^''  ^*^^«'^^«' 

^^(ti.  distance  traversed;  W-.^;L^;rZ 

may  be  mcreased  indefinitely  by  taldng  P  larg^  enough  tS 

case,  asvelocity,  time,  or  space  is  gaiZa,  poS  /    Zol  "  A  It 

leceives.  A  bank  will  give  you  in  exchange  for  a  fiftv-dolkr 
note  fifty  one-dollar  notes;  or,  for  fifty  one-dol,ar  nofes  "/ 
posited  successively,  it  will  return  toyou  a  fifty-dollar  note  Tn 
a  similar  manner,  if  you  aonlv  tn  n  Ln  i  •  ^^ 

to  move  50  lbs    1  n  ^  '""^  ""  P^^^''  sufficient 

In  our  v^liscussion  hitherto  we  have  io-nm-«^  tu^  •  x        ,       . 

--.,.1-,.,..  „  „....,  „5';«;  i'Ji'S';  "vt 

wo*  to  be  done  by  the  ,„.,cl,i„e  is  concerned.    Let  I  re  ,« 

.acne,  as  .o;,.ed  in  i^;  ^  tfXS:,' b^j:  '°' 

(2)  P2)=Wt«-fr; 
that  is,  the  work  applieU  to  a  machine  i.  e.ual  to  the  effective 


m 


1     ■ 


146 


t)YNAMICS. 


1:^  ).: 


|:v 


hi 
f'2 


» 


work  plus  the  internal  work  done  by  the  machine.  So,  that  su 
far  fl-om  any  machine  being  a  source  of  energy,  as  is  sometimes 
enoneously  supposed,  no  machine  practically  returns  as  much 
energy  as  is  applied  to  it. 

By  division.  Formula  (1)  Pp  =  Wtv  becomes       ^ 

(3)   ^=-^ 

i.e.,  weight    :  power   :    :  the  distance  through  which  tfie  power 
moves    :  the  distance  through  which  the  weight  is  moved  in  the 

same  time.     Prob- 
lems pertaining  to 
machines  may  gen- 
erally be  solved  by 
Formula    (3),  and 
afterwards  suitable 
allowances  may  be 
made   for   the    in- 
ternal work  done. 
Thus,  suppose  that 
P  (Fig.  99)  is    10 
lbs.,  and   it  is  re- 
quired to  find  what 
weight  (W)  it  will 
raise.      By  experi- 
ment, and  also  by 
geometry,  we  find 
that  P  travels  8  ft. 
ft      rp.  ,,^,      ,^  while  W  travels  4 

The  20  lbs.  in  W  ,8  just  sufficient  to  balance  the  10  lbs.  in  P- 
anything  less  than  20  lbs.  will  be  raised. 

It  18  to  be  observed  that,  as  we  saw,  §  89,  work  is  not  always 
or  even  usually,  expended  in  raising  a  weight,  but  in  overcom^ 

tlm«.  .7";  ''  '         "■''  ™''''^'  »»t«'pret  Formula  (3) 

thus  .  resistance  :  power  :  :  the  distance  through  which  the  powei 
moves  :  the  distance  through  which  the  resistance  is  overcome 


QUESTIONS  AND  PllOBLBMS. 


147 


QUESTIONS   AND    PROBLEMS. 

1.  If  the  power  applied  to  any  machiue  is  2^  and  It  r,n,r»o  «,ui. 

velocity  Of  10-  per  second,  wi^  what  velocity  InTZTrZjZ: 

n,«t,       u  '  """""'"S  ^'''■''"Sh  a  space  of  lOQm,  i^.  paoable  of 

moving  how  many  kilograms  through  a  space  of  2".?    What  adva^t^e 
would  be  gained  by  the  use  of  the  machine  ?  advantage 

3.   Watch  the  movements  of  the  foot  in  working  the  treadle  of  a 
sewing-machine,  also  the  movements  of  the  needfe  Tn  sewing    and 
determine  what  mechanical  advantage  is  gained  by  the  machine  ^' 
J^  n^r^"  three  levers,  as  in  Figure  98;  and,  calling  the  distance 
(ab)  of  the  po>.er  from  the  prop  the  power-arm  of  the  lever  and    he 

eCimenullout^  "^-'*  ^^^  *^^  P-P  the  ..-..  J^^e^fy  by' 
experiment  the  foUowmg  special  formula  for  levers :  — 

.^=.£  _  power -arm 
P     w     weight-arm" 
K.B.  — EqulHbrium  must  first  be  established  bctwopn  th^  ♦„„ 
lever,  by  placing  weights  on  the  8hort  arm.  *  *^'*  """^  "'  *«  «"* 

6.   Ascertain  the  advantage  that  may  be  gained  by  each  lever 

a  power  oT2V:r:?"^" '  ""''''  ^""«*  *^«  P-P  ^  P'aced  in  order  that 

end  may  move  4k  at    -^— ^— — —         Slg.89. 

the  other  end?   What 

will  be  the  pressure 

on  the  prep? 

7.  Show  that  the 
results  obtained  in 
the  last  problem  are 
consistent  witii  the 
third  law  of  parallel 
forces  (§72). 

8.  What  advantage 
Is  gained  by  a  lever, 

when  Its  power-arm  ^  ^^^^^^^^^^^^^^ 

Is  longer  than  Its  weight-arm?    What  wsIT^^^^^^^^^^^^ 

9.  Two  weights,  of  6^  and  20^7*:  .'  ^'^ht-arm  is  longer? 

lever  70- long    Where  mu^Mh!;."'f'"^'^  ^•"^^  '^^  ^^<^^  of  »- 
,ft    „.,    .  ^    ,    "^'^^"'"^t  the  prop  be  Placed  thnf.th»v!Ti-»vh«i=,-, 

th.  Otter  side  of  JfulirClu  W  IT U      '"'''''''^  '  """'"  "^"' 


!i 


i''  if 


fi  i 
fli 


I  it 


148 


DYNAMICS. 


II'  uZ7T  ''?  ""'^'  ""*  '  ''''■  "'  *^^  ^'*^  *h«  «''^™o  steelyard  ? 

14.   How  many  meters  must  the  power  travel  (Vi^r   u^n^  t        •       , 
bucket  from  a  cavity  10".  deej.?  ^     ^         ^  ^"  ''''"^*=  ^^'« 

16.    (a)  lu  the  train  of  wheel.  (Fi...  loi),  if  the  circun.ference  of 
^^«-  100-  the  wheel  a  is  30  in,  and  that 

of  the  pinion  6  is  4  in,  a  power 
of  1   lb.  at  P  will  exert  what 
force  on  the  circumference  of 
the  wheel  d  ?     (b)  if  the  cir- 
cumference of  the  wheel  d  be 
30  in.,  and  that  of  the  pinion  c 
6  in.,  the  power  of  i  lb.  at  P 
will  exert  ,vhat  force  on  the 
circumference  of  tlie  wheel  f? 
Wheel/be  40  in,  and  that  of  the  axle  .  rV^^''  -•'•^""'ference  of  the 
wm  be  nece^ary  to  prevent^t^lSl  :;t;:'t:::  '^^.Z:ZZl 

^^•^'*^-  weighs  llu.?     (rf)IfWhasa 

velocity  of  5  ft.  per  second, 
what  will  be  P's  \elocity? 

16.  Prepare  a  special  for- 
nmla  for  the  solution  of  prob- 
lems pertaining  to  the  wheel 
and  axle. 

17.  The  weight  W  (V\>r. 
102),  In  traversing  the  in- 
clined  plane  AB,  only  rises 
thron-h  the  vertical  hight  CB, 
while  P  must  move  throiigli  a 
distance  equal  to  \B.  J.ct 
L  represent  t;  .  .t],  of  an 
inchned  plan.^   ii.,i  i    ?  s  hight 

i«».  A  Skid  12  ft.  long  rests  one  end  on  a  car    t  f  f    i  i  , 
o«,cr  c,„,  „„  t„o  ,ro„.d.    w„„.  force  ,„„  ."a^  ,  l^  ^  ^J^l 

».  During  one  revolution  a  screw  aUvanco.  »  distance  e,ual  to  the 


QUESTIONS   AND   PKOBLEMS. 


149 


distance  between  two  turns  of  the  thread,  measured  in  the  direction  of 
the  axis  of  the  screw.    Suppose  the  screw  in  the  letter-press,  Figure 
103  to  advance  ^  ,n.  at  each  revolution,  and  a  power  of  25  lbs.  t^  be 
applied  to  the  circumference  of  the  wheel  6,  whose  diameter  is  14  in 
What  pressure  would  be  ex- 
erted on  articles  placed  be- ^- 103. 

iieath  the  screw.  [The  cir- 
cumference of  a  circle  is 
S.U16  times  its  diameter.] 
20.  The  toggle-joint  (Fig. 
104)  is  a  machine  employed 
where  gi-eat  pressure  has  to 
be  exerted  through  a  small 
space,  ci  ia  punching  and 

shearing  iron,  and  in  print-  

iBg-presses,  in  pressing  the  types  forcibly  against  the  paper.     An 

illustration  may  be  found  in  the 


Fig.  103. 


joints  used  to  raise  carriage-tops. 
Force  applied  to  the  p,g,  j^^ 
ioint  c  will  cause 
two  links  ac  and 
be  to  be  straight- 
ened, or  carried  for- 
ward to  d,  while  the 
guides  move  through 
a  distance  equal  to 
(ac  +  be)  -  ab.  It 
dc  =  lO™,  ab  =  98""^ 

,,  ^  and  ac  +  bc=  lOOcm,  i i 

then  a  force  of  80.  applied  at  c  would  exert  what  average  pressure 
oi.  obstacles  in  the  path  of  the  guides?  pressure 

21.    Show  that  the  hydrostatic  press  conforms  in  its  operations  to 
the  general  law  of  machines.  I'citt.iuiis  lo 

§  100  b.  Moments  and  Equilibrium. -We  often  find  it 
convenient  to  consider  the  tendency  of  a  force  to  produce  rot.- 
.on  round  an  axis  wliicli  is  at  right  angles  to  the  plane  in  which 
the  force  acts.  Take,  for  example,  any  one  of  the  levers  in  Fi^ 
98,  the  force  P  has  a  tendency  to  produce  rotation  about  the 
point  b  m  one  direction,  while  W  has  a  tendency  to  produce 
rotation  about  b  m  tiie  opposite  directiou.    If  the  lever  is  just 


If  1 

II 


(i  is  j 

n'''l 


1^ 


150 


DYNAMICS. 


ii ;« 


MM. 


balanced,  these  t„o  teudeueios  a™  cvideoU...  oc,„a.  and  op- 

This  tendency  of  a,  force  ic  ,>;oduce  rotation  about  a  noinf 
■s  called  the  moment  o(  that  foroe  with  i-esnect  t„  TT      '        ' 
-«  b,.ie«,,  the  .no,„e„t  of  that  J^  l^  1°     2""''  '" 

F,„„.  c::„.„„en,s  a!,„ad.v  umde  >,i.h  levc-s  i-'  „i,  'he  seen 

p«..w;..«f™„o..,t;::h.":-^r:rti^^^^^^^^^^^^^ 

we  take  a.  tm  measure  of  the  moment  of  F  about  O  iul       ^' 

and  opposite  to  the  momeut  of  a  force  Q  about  o",."  "T^ 
When,   in  a  system  of  forces,  the  moments  about   n   point 

at:t::::o-t-:!:rcr:t:rrt:ar^^^^ 

n.on,o„ts  about  O,  of  those  fo,ce,  of  the'^jslTu  h  tl" 
K  the  moments  of  a  system  vanish  about  a  r>oi„t  (l      i    .  ■ 

iX:r  ^^"»  '^^  "■»  -  --'  o'  '^e'riant'  :m:: 

If  the  moments  of  the  system  vanish  al)on<  r>  n    i    , 
about  P,  What  do  you  .no.  about  th^ret, l^'cT  hit  Z^ 
If  the  moments  vanish  about  each  of  three  po^       O     '   tt,  n 
what  do  you  know  about  the  resultant  ?    If  o  .l,  o         ^' 

in  the  same  s,....;ght  line,  what  do  you  k     I "    .  ,  ,,',.?  "I'f  ""i 
Can  the  line,      .  .tion  of  the  resultlnt  of  ,",;"", 

other  than  a  s„.„ht  line?    If  a  svsten,  .      .brcL  L  in 


libriura,  that  is,  if  the  forces    are' such 


ountoract  ouo 


op- 


MOMENTS   AND   EQUILIDRIUM.  15l 

ar^othcr,  and,  taken  together,  produce  no  eflfect,  is  there  any 
point  about  which  their  moments  do  not  vanish? 

If  the  resolved  parts  (§  70)  of  a  system  of  forces  alon- a 
line  m  one  direction  are  together  equal  to  the  resolved  parts^of 
the  same  system  along  the  same  line  in  the  opposite  direction 
the  resolved  parts  of  that  system  are  said  to  vanish  along  that 

If  the  resolved  parts  of  a  system  of  forces  vanishlilong  the 
hne  A  B,  can  that  system,  as  a  whole,  produce  any  motion 
along  A  B  in  either  direction.  In  the  above  case,  what  do  you 
know  about  the  resultant  of  the  system? 

If  the  resolved  parts  of  the  system  vanish  along  A  B,  and  also 
along  C  D,  what  do  you  know  about  the  resultant?     If  A  B  and 
C  D  are  not  parallel,  what  do  you  know  al)out  the  resultant? 
Can  the  hue  of  action  of  the  resultant  be  at  right  angles  t« 
each  of  two  lines  which  are  not  parallel  to  each  other?    If  a 
system  of  forces  is  in  equilibrium,  is  there  any  line  along  which 
their  resolved  parts  do  not  vanish?    If  the  resolved  part^  of  a 
system  vanish  along  each  of  two  lines  not  parallel  to  each  other 
IS  the  system  necessarily  in  equilibrium?     Is  a  couple  (§  73)  in 
equ.hbrium?    Do  the  resolved  parts  of  a  couple  vanish  along 
each  of  two  lines  not  parallel  ? 

From  a  careful  consideration  of  the  foregoing  questions  the 
pup.l  will  see  the  truth  of  the  foUowiug  propositions,  which  are 
very  important :  — 

EQUILIBRIUM   OF    FORCES    ACTING    IN  THE    SAME  PLANE. 

1 .  If  a  system  of  forces  is  in  equilibrium  the  resolved  parts  of 
the  system  vanish  along  any  line  tvhatever,  and  the  moments  of 
the  system  vanish  about  any  point  whatever. 

2.  Jfth^  moments  of  a  system  of  forces,  all  in  the  same  plane, 
vanish  about  each  of  three  points  not  in  the  same  straight  line,  the 
system  must  be  in  equilibrium. 

3.  If  the  moments  of  a  system  of  forces,  all  in  the  same  plane 
vanish  about  one  point,  and  their  resolved  parts  vanish  alo^ig  eoc/I 


»%;• 


If  III 

i 


152 


.^Dynamics. 


If  it  is  known  that  a  system  of  forces  is  in  equilibrium   the 

fact  that  the  system  is  iu  equilibrium.     Why?  ^ 

Example  1. 

A  uniform  beam, 
A  B,  20  feet  long, 
weighing  300 
lbs., rests  with 
one  end  against 
a  smooth,  verti- 
cal   wall,   C  D, 
and    the    other 
«f')donasmooth, 
f.orizoutal 
plane,  C  B,  this 
end   being    tied 
by  a  cord,  C  B, 
16  ft.  long.    In- 
vestigate     the 
forces     acting 
The  beam  Is  evidently  acted  uoon  hv  fn„..  f  "^""  *''^  ''''^'"• 

own  weight.  300  lbs.,  which  since  th.h  •'''  ""'"'^^  •"  ^'''  ^'' 
posed  to  act  at  K,  the  Jd  1  ;: U  :f  1"b  "2i";lT'  ''''' '^  •^"'^■ 
string  C  B, .  lbs.,  acting  at  B  in^he  diritn  b  C  sf t^"'"  °'  ''" 
the  wall,  X  lbs.  acting  at  A  at  rWU  an'  os  to  tb.       n  ^''''"''^  "^ 

smooth;    4th,  the  pressure  of  thl  n  '''''"'  ''"^«  "'«  «'«»  '« 

angles  to  the'  floor^S^ L^;  if  rio^h'^'  '^"'"^  '^^  ^  ^  ^'^"^ 

::;u:s:;:' !!^^^"^ ''- «-'  ^-^->"-  -^^ov^  we-ha;;';.;:^;;:::!;: 


MOMENTS  AND  EQPILIBEIOM.  I53 

_^__B.c.„se.her„„,ve<,p„.,„,  .,,  „,^„  ,„„,  ,,„__^  _  ^^^_^^^^_ 

Because  the  resolved  parts  vanish  along  a  vertical  line. 

y  =  300 (2). 

Because  the  moments  vanish  about  any  point  (say)  H 
2BH=:300OH ^3^  ' 

Iherefore.  substituting  in  equation  (3)  we  have  ^ 

12  z=  ;J00  X  8 

300  X  8 
^= j^ — ^  =  200 

But  x  =  z 

.-.2  =  200 


Example  2.     Let  A 

B  (Fig.  F)  be  a  smooth 
inclined  plane,  tlie  angle 
A  being  30".        Let   a 
heavy  particle  placed  at 
T>  be  kept  at  rest  by  a 
string,  D  B.   Investigate 
the  forces  acting  on  this  A 
particle.      The    particle 
is    evidently    acted   on 
by  three  forces,  namely  : 
1st,  its  own  weight,  lOO 

ltri'nr?ihf '  f  "'''^^'^^  ^''•"^''"y  ^"^"^^'•^ '  2c1  the  tension  of  the 
n!'  ^t  D  '  "h     •'  '"  ""'  ""  ° '  •'''  ''''  P'-^««"^«  «f  t'^e  plane   y  lbs 
the  pfa:e  ''  "''  ""^'^  *'^  P'^"«  '«  --*^'  -*'"«"  »*  right  a^^es  i 

A^r?,J^ '""'"'' ''^'''' '"""'"^  "'''''^ ""'' '''^^  "^^  ^<i  the  angle 

X  =  100  X  i  =  50. 
^Because  the  resolved  parts  vanish  along  D  H.  and  the  angle  E  D  H 

y  =  100X^-2  =  50^3 


154 


DYNAMICS. 


To  ai)ply  the  above  piopositioo  correctly,  the  pupil  must  be 
esreful  to  take  note  of  all  the  forces  of  the  system  in  equi- 
I.brmm,  and  to  make  no  m---  h.'  .  «  .pressing  the  resolved  parts 
and  momenta.     Resolved  parts  are  discussed  in   §§  70  and  716. 

QUESTIONS    AND    PROBLEMS. 

a  Lio^rlir.  ""'''  '"  *"^''  *"' '^"^"°"  °"  "»«  ^«*=*  '^^'  tl^«  moments  of 
wiTh    ho  .''  •"  ^^"'"''••'"'»  v«"-h  about  auy  point  whatever. and 

wish  the  equation  not  to  involve  a  particular  force  of  the  sys  em 
Where  should  you  choose  the  point?    If  you  wish  the  equation  notTo 

u^rts  of  th  """"^  ^^  *"  '''"**'°"'  *''^''*'^  °"  ♦^'^  f»^*  '^^'  the  resolved 
paits  of  the  system  vanish  along  any  line  whatever,  not  to  involve  a 
particular  force  of  the  system.  .  V*  line  .borld  you  choo« 

2.  A  uniform  beam  37  feet  V  .^  -^  ..[ang  400  lbs.,  rests  with  one 
end  against  a  smooth  wall,  and  the  other  end  on  a  smooth  Jo     th  s 

iZxT,  Tr^  '^  "  ''''''  ''  '''''  ^°"^  ^°  ^  ^'^  -t  the  bottom  ofUe 
wall ;  find  the  tension  of  the  cord, 

3  In  Example  2,  if  the  weight  of  the  beam  acted  at  a  point  i  of  its 
length  from  i  he  lower  end ;  And  the  reactions  of  the  wall  and  iir 

4.  A  beam  A  B,  ^eighuig  120  lbs.,  a -ting  at  its  middle  point  is 
made  to  rest  against  a  smooth  v  rtical  wall  and  on  a  smooth  floo  by  a 
force  apphec  .rizom.ily  to  ti,  -bot;  find  the  force  if  the  inclination 
of  the  beam  is  ^n)  30^,  (6)  45°,  (c)  60°.  '"cunation 

6       In  Example  4,  if  the  weigh .  .1  the  beam  acted  at  a  point  ?  of  its 

SioV 7 ."» ':)»"""  ■■' '°"°' '"  '"="'-"°" "' «"""»-  -- 

''•      Taking  the  incllnatl,     oft,     beam  a*,  in  p^o„.^i„  ^    a    ,     , 
a  weightof  120  lbs.  must  be  ^^aspended  IXt  I^-^ ttll rce^^: 
ing  m  IbT  "  ""'  '"  ^''^"^'^  ''  "^^'  '^'^"^  '^^•"^  -^^-"'   -d  weS- 

8.      A  uniform  beam,  weighing  60  lbs.,  rests  wifh  np.  ....^  „^-._-. 
peg  in  a  smooth  horizontal  plane,  and  the  other  end"  on  a  "waif"  The 
point  Of  contact  with  the  wall  divides  the  beam  into  parts  as  3     I 


QUESTIONS  AND  PROBLEMS. 


156 


tlon  of  the  beam  being  (a)  30°,  (i)  45°,  (c)  60°. 

9       What  relation  must  tl.e  moment  of  the  whole  weight  of  a  body 
weights  of  Its  several  parts  about  the  same  line? 

nnint' n  ,.^^*'»^^''*1«  ^""^  «f  the  moments  of  several  forces  about  a 
pomt  or  hne  Ks  understood,  the  excess  of  the  sum  of  the  positive  mo 
ments  over  the  sum  of  t.  negative  n.on..nts.  It  is  customary  to  con- 
sider a  moment  positive  wi.en  the  tendency  to  rotation  is  in  the  direction 
opposi  e  that  m  which  the  hands  of  a  watch  n.ove  when  you  are Tol 
^g  at  Its  face,  and  negative,  of  course,  when  the  tendency  to  rotation 
Is  In  the  same  direction  as  the  hands  of  the  watrh. 

10.  How  may  you  apply  the  answer  to  Question  9  to  find  the  distance 
of  the  centre  of  gravity  of  a  body  from  a  given  line,  when  ,he  weights 
of  the  several  parts  of  the  body  are  given,  and  the  distance  of  the 
centre  of  gravity  of  each  part  from  that  lin.  is  also  given? 

gravity" (§'?!;). ''''^*''  ""^  ^  ^""^^  ""^^  ^'  '"^P°^^^  '"^  ^'^  *'  "«  ««°t'-«  «f 

11.  How  may  you  apply  the  answer  to  Question  10  to  tind  the  posi- 
ti    .  of  the  centre  of  gravity  of  the  body  in  Question  10? 

Three  uniform  rods  are  placed  so  as  to  form  a  right-ancled 
\so8celes  triangle,  the  longest  being  8^2  feet;  find  their  C.  G 

13     A  heavy  tapering  rod,  weighing  160  lbs.,  balances  about  a  point 
4  f.-et  from  the  heavy  end,  when  a  weight  of  30  lbs.  is  attached  to  the 
he  other  end;  find  the  point  about  which  it  will  h.,lanc.  if    he^  iS 
Is  removed.  "^" 

14.  Four  weights  of  5,  7,  9,  and  11  lbs.  are  placed  a-  the  comers  of 
a  square  plate  weighing  12  lbs.,  whoso  side  is  10  inches-  find  the 
distance  of  the  C.  G.  from  the  centre  of  the  plate. 

1«.     Weights  of  4,  6,  8,  7,  3,  2,  13,  and  1  lbs.  are  placed  at  the  cor 

C.  (j.,  the  side  of  the  square  being  16  inches. 

18.    Aumfonnsquare  plate  whosesidcisl0inches,andweightl21bs 
has  a  weight  of  18  lbs.  attached  to  one  co  ,.er ;  where  must  it  be  sus' 
pended  by  a  cord  so  as  . o  rest  horizontally? 

17.    A  square  table,   weighing  40  lbs.,  rests  on  four  legs,  one  at 
each^  corner.    Can  you  determine  the  pressure  on  each  leg?    If  so! 


'•  .11 

E    '-I 


m 
ill 

i        « 


166 


DYNAMICS. 


18.  From  a  circular  plate  whose  radius  is  8  inches,  a  circular  plate 
whose  radius  is  4  inches  is  cut  away,  the  distance  lietween  tl^e  two 
centres  is  two  inches;  find  the  centre  of  gravity  of  the  remainder. 

„  ?K  ^?™.*  "'''^''""  '^'''''"^^'"  ^^'^^'  ^'^o^^  diameter  Is  10  inches, 
another  disc,  having  for  its  diameter  the  radius  of  the  first  circle,  is  cut 
away;  find  centre  of  gra\ity  of  the  remainder. 

20.  From  a  circular  disc  whose  diameter  is  D,  a  circular  disc  whose 
diameter  is  d  is  cut  away;  find  tlie  centre  of  gravity  of  the  remainder, 
tne  distance  between  their  centres  being  a. 


CHAPTER    III. 
MOLECULAR   ENERGY.  -  HEAT. 


XVII.     WHAT  HEAT  IS. -SOME   SOURCES   OP  HEAT. 
In  the  preceding  pages  the  theory  of  heat  has  been  several 

§  102.  Mechanical  motion  convertible  into  heat  -F, 

SLt-    Zi  Tr  ""■""  ■"°«'  '»»'  ""O"  »  -P°"^  re'vln,  a'; 

.r  .t::  r.:,:3r.'r  ,::,■=:;  zz 

checm  Ucomes  heat.  When  tl»  brakes  are  applied  T  he 
wheel,  of  a  rapidly  „,ovtog  railroad  train,  its  motion  is  a^e^" 
verted  ,„,<,  heat,  ™„el,  of  which  may  be  found  in  the  wheTls 
brake-bloeks,  and  rails.  The  meteorites,  or  "  shooting.rr^  " 
wh,ch  .are  seen  at  night  passing  through  the  upper  afr  some 
™es  strike  the  earth,  and  are  found  I  be  stene'  heawTt 
l.ght-g,vmg  state.  Thev  beeome  heated  when  they  reaeh  our 
a  mosphere,  m  conscquenee  of  their  motion  being  cl>eck<^  by 
the  resistance  of  the  air.  ' 

§  103.    Heat  convertible  int/^  «,«„>,»_,•— ■  _.», 
Expenment.    Take  .  .1„„  g,a.,  «.";k-A,'Fig7re"7;n,,rhT?uT. 
with  water,   ftt  a  cork  air-.,,,,..  ,„  ,.,  neck.     Perto™^  X  c"r" 
■  A  lto<Kl  w.,  B  „.k.  .  crt  „|r.„,M  1.  B  „„t  „  ,„  „„,^  ^„„„ 


ii 


!l 


•  l.'r'l 

Iff?  I 

;       '"pl 


'■4 


H  • 


158 


MOLECITLAR    ENERGY.  —  HEAT. 


IL 


^    Here  heat  produces  mechanical  motion,  and  does  work  in  rai^ 
-g  a  weight  in  opposition  to  gravity.     Ever,  steam  ^gineTa" 
Pi.  10.  hm-eyu,ine.     AH  the    power  of  steam  consists 

in  its  heat.  The  steam  which  leaves  the  cylin- 
der of  an  engine  (see  §  148),  after  it  has  set 
the  piston  ;n  motion,  is  cooler  than  when  it 
entered,  and  cooler  in  proportion  to  the  work 
done.  Furthermore,  it  will  be  shown  (§  145) 
that  heat  and  work  are  so  related  to  eadi  other 
that  a  definite  quantity  of  the  one  is  always  equal 
to  a  definite  quantity  of  the  other. 

Now,  when  the  appearance  of  one  thin<r  is  so 
connected  with  the  disappearance  of  another, 
that  the  quantity  of  the  thing  produced  can  be 
calculated  from  the  quantity  of  that  which  dis- 
appears, we  conclude  that  the  one  has  been 
formed  at  the  expense  of  the  othor,  and  that 
they  are  only  di'^erent  forms  of  the  same  thing. 
We  have,  therefore,  reason  to  believe  that  heat  is  of  the  same 
nature  as  mechanical  energy,  i.e.,  it  is  only  another  form  of 
kinetic  energy.  j  ">-  uj 

r  "^  ,.^***  defined.  -A  body  loses  motio,.  i,>  comrauni- 
ca  ing  ,t  (5  67,  The  Lammer  descends  and  strike,  the  I- 
V.1;  lis  motion  ceases,  hut  the  anvil  is  not  sensibly  moved; 
the  only  observable  effect  produced  is  heat.    Instead  of  the  pro' 

f„'rr.h""""°;; "' "'"  "'""■""  ■"  ^  ""*•  "■««=  - "«".  "oc^rd. 

■ng  to  the  modern  view,  an  increased  vibratory  n.otion  of  the 

ma,..„fe,  that  compose  the  hammer,  -a^ere  cLn,e  of  ItZ 

n  W  andlocalU,.     Of  course,  this  latter  motion's  invisibTe! 

.    "~  ~: — ' '"  ^^'"^  ''^"'  '^  molecular  molion.    A  bodv  is  heated 

by    avmg  the  motion  of  its  molecules  quickened,  and-cooledty 
parting  witli  some  of  its  molecular  motion. 


HEAT    DEFINED. 


159 


n,i.,\,  generated  by  chemical  action. -Experi- 

^ono  f      T^*"-^  ""  ^'^^''  '''^-^''^''  "^'^  ^""  «f  ^«ld  water,  and  pour  Into 
can  th  Tn  r'"'"'  "'  '"'^^'""'^  '^^'^-    W'^^^t  '«  the  effect?  Whence 

thT  Ti,  "r""'  ™"'""'"  ""^'""  ^"^^^    ««-  •^o-  the  volume  : 

oped      The  invisible  oxygen  of  the  air  combines  with  the  vari- 
ous fuels,  such  as  wood,  coal,  oils,  and  illuminating  gas,  and 
gives  nse  to  what  we  call  burning  or  combustion,  by  which  a 
large  amount  of  heat  is  generated.     In  all  such  case;  the  heat 
18  generated  hy  the  combination  or  clashing  together  of  mole- 
cules o    substances  that  have  an  affinity  {i.e.,  an  attraction) 
for  each  other.     Before  their  union  they  are  in  the  condition 
of  a  weight  drawn  up;  while  approaching  each  other  they  are 
like    he  falling  weight;  and  when  they  collide,  their  motion, 
like    hat  of  the  weight  when  it  strikes  the  earth,  is  converted 
into  heat      The  chemical  potential  energy  of  the  molecules  is 
converted,  in  the  act  of  combination,  _to  molecular  kinetic 
energy,  —  into  molecular  motion. 

§  106.     Origrin  of  animal  heat  and  muscular  motion  — 
The  plant  finds  its  food  in  the  air  (principally  the  carbon  dioxide 
m  the  air)  and  in  the  earth  in  the  condition  of  a  fallen  weicrht  • 
but,  by  the  agency  of  the  sun's  radiation,  work  is  performed 
upon  this  matter  during  the  growth  of  the  plant;  potential  energy 
18  stored  in  the  plant, -the  weight  is  drawn  up.     The  animTl 
now  finds  its  food  in  the  plant,  appropriates  the  energy  stored 
in  the  j)lant,  and  converts  it  into  energy  of  motion  in  the  form 
of  heat  and  muscular  motion.     The   plant,  then,   may  be  re- 
garded as  a  machine  for  converting  energy  of  motion  'received 
from  the  sun  into  potential  enngy ;  the  animal,  as  a  machine 
lor  transforming  it  again  into  the  energy  of  motion 


1« 


R- 


i  li : 


r£.<i 


> 


160 


MOLECULAR   P^NERGY.  —  HEAT. 


I 
U 


II  i 


I'i    I 


§  107.     The  sun  as  a  source  of  energy.  -  Not  only  is  the 

un  the  source  of  the  energy  exhibited  iu  the  growth  of  plants, 

as  well  as  of  tlje  ..uscular  and  heat  energy  of  the  anirnul'but 

IS  the  source,  d.rectly  or  indirectly,  of  very  nearly  all  the    ner^y 

en^i^oyed  by  „.an  in  doing  work.     Our  coal-bedsf the  results;' 

the  deposit  of  vegetable  matter,  are  vast  storehouses  of  the  sun's 

energy,  rendered  potential  during  the  growth  of  the  plants  n.any 

ages  ago.     Every  drop  of  water  that  falls  to  the  earth,  and  rolls 

nowT7of"t       "::  -"f'buting  it.  n.ite  to  the  unbounded  water- 

powe   of  the  earth,  and  every  wind  tiiat  blows,  derives  its  power 

directly  from  the  sun.  ^  ^    u^  power 

If  a  man  were  to  make  use  of  the  ocean  tides  for  drivin.. 

TZ7  r  ""'  '  1"  "^'"^^-"-g^  •^--ived  from  what  soured 
B3  the  friction  ol  the  tides  against  the  coast  the  water  and 
and  are  warmed.  What  is  the  source  of  this  energy?  t 
tins  source  inexhaustible?  U  it  increased  itself  fSn  any 
other   source?     If  not,    what  must  be  the  effect  of  this   co  ' 

t":?  "^""  '''•     ''  ''''  '''^'"^'  ^«-^  ^-  ^«  ^ound  outsMe 

XVIII.     TEMPERATURE. 
§108.     Temperature  defined. —If  bodv   A  Ju  i         i.  • 
co„.ac.  with  .„.,,  B,  „„„  A  l„.os  ,„k,  b'L r  f„  t,    t, t ^A  Z 
a,d  to  have  ha.I  o,i,n„an,-  „  higher  ,nnpcra>.,re  thu, 
m.thor  body  gai„»  or  loses  the,,  both  l,ad  the  sa„,e  tcLra 
u  e      Temperature  is  tke  state  .^f  a  M,  e.^smereU  JZfit 
ence  to  Us  pou,erof  c.m„„„{cunni,  Ma,  lo  or  r.c«vi„,  hen,   rL 
other  W«.     The  direction  of  ,  he  flow  of  heat  deter,'i„e»  wh 
of  two  bod,es  has  the  higl,er  temi,e,ntn,c 

It  may  be  n.athematieally  demo„st,ated  that,  if  tl,e  ave,-a.re 
k,net,e  energy  of  eaeh  u,oh.oale  of  A  is  eaoil  to  "°  •""■"'«'' 
kuetie  energy  of  each  n,o,ee„,e  of  B,  «.«;":;:„  7  ..Ta?: 
brought  into  contact  the  inoleeales  of  A  wjii  „-.»!■..  '■        T 

those  of  A.     Hence  we  may  say  tlmt  two  bodies  have  </«  same 


TEMPERATURE. 


161 


temperature  wh.n  the  average  kinettc  energy  of  each  molecule  of 
the  other'  '"  ''*'  *'"'''^'  ^''''^''  '""'^^  ^-^'"''^  '^^^'''^'  ^-^ 

heit^^^'-n'^T^^''^*''''^  distinguished  from   quantity  of 

neat.  -  Ihe  tonu  temperature  has  no  refeivuee  to  quantity  of 

heat.     If  we  mix  together  two  equal  quantities  of  a  substance  at 

^he  same  temperature,  the  temperature  of  the  mixture  is  not  the 

sum  of  the  temi)eraturos,  -  it  is  not  greater  or  less  tlian  tliat  oi 

either  before  they  were  mixed  ;  but  evidently  the  mixture  contains 

vv.ce  as  nmcli  heat  as  either  alone.     If  we  dip  from  a  gallon  of 

boilmg  water  a  cupful,  the  cup  of  water  is  just  as  hot,  i.e., 

has  the  same  temperature,  as  the  larger  quantity,  although  of 

cou,-se  there  ,s  a  great  difference  in  the  quantities  of  heat  the 

two  bodies  of  water  contain.     Temperature  depends  upon  the 

average  lanet^c  energy  of  the  individual  molecule,  while  quantity 

of  heat  depends  upon  the  average  Kinetic  energy  of  the  individual 

molecule  multiplied  by  the  number  of  molecules. 

XIX.     DIFFUSION  OF  HEAT. 

There  is  always  a  tendency  to  equalization  of  temperature; 
tha  ,s,  heat  lias  a  tendency  to  pass  from  a  warmer  body  to  a 
colder  or  from  a  warmer  to  a  colder  part  of  the  same  body, 
until  there  is  an  equilibrium  of  tempeiuture. 

If  you  put  your  hand  in  contact  with  a  body  at  a  lower  tern- 
perature  than  your  hand  molecular  kinetic  energy  passes  from 
your  hand  to  the  body,  and  you  experience  a  sensation  which  leads 
yon  to  say  that  the  body  feels  col.l.  If  the  body  is  at  a  higher 
ten,i,erature  than  you,  hand  your  hand  gains  molecular  ki.^tio 
nierg.v,  and  you  experience  a  sensation  which  leads  you  to  say 
that  the  body  feels  warm.  7  h.  intensify  of  the  sensation  depends 
upon  the  rate  at  which  your  hand  loses  or  gains  molecular  L.fic 
energy.  In  other  words,  it  depends  upon  the  rate  at  which  the 
temperature  of  your  hand  falls  or  rises.  The  rate  at  which  the 
temperature  of  your  hand  changes  tvill  depend,  of  course,  upon  the 


,m 


U 


il  ■ 


til 

'"ii'f 


162 


MOLECULAR  ENERGY.  —.  HEAT. 


tnie  ofthatpart  oj  the  body  in  immediate  contact  wi'h  it. 

abouU^°:  Io.!?°  nfrr*'°^;  ~  ^''"^""'''"*  »•   ^'"--  on.  end  of  a  wire 
Api^yonrZ^^V^';^'""''' '''''''''''  "-  «^'-  -»I  i"  tl.e  hand. 

Pla'ces  ot- Lot 'r'   ?""^"'  "^  -equally-heated  bo.ly,  fron. 
Zton    2t       r   i^^---f-»-ver  temperature,  is  called  c..- 

enld    .h        !,  ""''"  ^"  *^'  ^^""^  '^^^«  their  motion  nuiek- 

ened,  th  y  strike  their  neighbors,  and  quielcen  their  motion    the 
latter  .n  turn  quicken  the  motion  of  tl,e  next,  and  so  0,?;. 
some  01  the  motion  may  be  linally  communiclte.)  to  th    'h     d 
and  creates  in  it  the  sensation  of  heat. 

Experiment  2.     Hold  wires  of  dhlbront  uwfnU  nf  ti, 
also  a  glass  tube,  a  pipe-stem   ete    i  h  '  ''"'"^  ^'^"^'"'- 

:;^::.Ser-— --— ^ 

probably  fin;:;;:",;"  a  r  rs::rrr '"  "^^^^"'"'  ^-^^  ^^'" 

perature.     Place  your  ban     on  tl,o  ^    ^'  ""^'■^•'  ""^  '^"^^'  *^''"- 

lmveverydiflc.en   t    ,.Su"s      ivTr^"''"^  *'"'^^-  ^^^^'^  '- 

wood.     Theironfeel     codlr  than  tZ    '"T"    '""  ""'  ^^  '^'"^"^  «^ 
iron  and  the  other  o    th    woo.l  f  '^°''''-     ^^''^  «'"^  '•'^"^'  «»  the 

mometertothe    n^^c  "late^i'T  T  f^T    '^^""  ^^'''^  ^'^  «-- 
still  atthesan.ue;.u"  at  r:P^:rH:^^^^^^^  '"""J'^-      ^'•^'  ^"^'-^ 

been  raised  by  contaet  with  yonZ^o^^^^'''''  "T'  """'  ""^ 
of  the  iron,   in  the   same   tinw/    i         !■    ^!         ''''''''''^"''^^ 
between  the  «ensatior:::pr:.  J^  H^';::^-^;-;'' '''--^ 
account  for  tlie  fact  itself?     1.  u  -, ,  bands .^     Mow  can  you 

dactor,  and  henc^  h    ^^^j,.^:;  ^  ^^S  ""^V'","""'  '^  ^  '^'"'  ™"- 

because  th.-.  heat  it  receives  from     b  ,  ""'  ''  '"''''^^^  ^^'"•'"^'^' 

other  parts  .>f  the  bockw  ,""      ''  ""'  '"'"^"'■^''•'  '^^^•'^^  ^o 

ndne  wlu.ther  wl't'L.^  ".;"'""  ;;'"'  ""  ^""  -.^«-t  to  d.-ter- 
.  --'  —'•••"'?-.  !Hut  r.-t,pi(iiy  or  iKjtr 

ftxpcnmeiit  4.     Twist  toL'otber  -it  rm,>  o.wi     •    •. 


"i  ft' 


OOifVECTiON. 


163 


seeing  ,.o.  far  J^n  rZioTt  wm  ^^  "^^^^  ^'^'^^'  ^^^^  «^-'  ^^ 

tl-gh  they  cliffer  widely  a^ongte^^^^^^^^^^^      '"^  ^°'^'"^^^^' 

tube  near  the  surfal  of  ^hh^^te^  Do        ™'''        ^  '"'  "''''  °'  "" 
you  find  that  the  heat  is  rapidly  or  slow-  ^^«-  ^'»- 

ly^^tmnsferred  to  the  lower  part  of  the 


Liquids,  as  a  class,  are  poorer  con- 
ductors than  solids.  Gases  are  much 
poorer  conductors  than  liquids.  It  is 
difficult  to  discover  that  pure,  dry  air 
possesses  an^  conducting  power      The  —  - 

y   muMug  or   heated  substances,  the  onerilion   5^  ^„ii   » 
convection  •  huf  fi,;c  t-         •  "I'erauon   is  callea 

not  necesaarilv  ««  «,      ,  f  ^''«  <^''^"veyai'ce ;  fluids  do 

ncceesanly,  a.  may  be  seeu  by  the  foUowiug  experiments  .  ■»- 


I 


1 


164 


MOLECtTLAR  EKERGV.  —  SEAT. 


Experiment  1.  Arrange  apparatus  as  In  Fig.  107.  Fill  tlie  larf'e 
beaker  nearly  full  of  water,  and  elevate  It  so  that  the  tip  of  a  Bunsen 
flame  may  just  touch  the  middle  of  the  bottom.    Fill  a  glass  tube  B 


Fig.  107. 


Fig.  108. 


With  a  deeply-colored  aniline  solution,  stop  one  end 
with  a  finger,  and  thrust  the  other  end  into  the  water 
to  the  bottom  of  the  beaker;  remove  the  finger,  and 
allow  the  solution  to  flow  out  and  color  the  water  at 
the  bottom  for  a  little  denrh.  Soon  the  colored 
liquid  immediately  over  the  flame  becomes  heated, 
expands,  and  thereby  becomes  less  dense  than  the 
liquid  above ;  consequently  it  rises  luu]  forms  an  up- 
ward current  through  the  colorless  liquid.  At  the 
saftie  time  the  cooler  liquid  on  the  sides  descends  to 
take  the  place  of  that  which  rises,  and  soon  the 
descending  currents  become  visible  by  the  coloration 
of  the  water.  By  this  means  heat  is  conveyed  to  all 
parts  of  the  liquid,  which  would  otherwise  become 
much  hotter  at  the  bottom  than  at  the  top  in  couse- 
quence  of  the  poor  conducting  power  of  water. 

If  a  glass  tube  C,  bent  as  shown  in  the  figure,  is 
filled  with  water,  and  introduced  into  the  beaker  so 
that  the  orifice  of  the  short  arm  shall  be 
just  beneath  the  surface  of  the  colored 
water,  the  colored  liquid  will  be  seen  slowly 
to  ascend  the  short  arm,  while  the  colder 
water  will  descend  the  longer  arm. 

Experiment  2.  Provide  a  tightly-cov- 
ered tin  vessel  (Fig.  108)  and  two  lamp- 
chimneys  A  and  B.  Near  one  side  of  the 
top  of  the  cover  cut  a  hole  a  little  smaller 
than  the  large  aperture  of  chimney  B.  Near 
the  opposite  side  of  the  cover  cut  a  series  of 
holes  of  about  7"""  diameter,  arranged  in  a 
circle,  the  circle  being  large  enough  to  ad- 
mit a  candle  without  covering  the  holes. 
Light  the  candle,  and  cover  it  with  chim- 
ney A,  which  should  be  outside  the  circle 
of  holes  Fasten  both  chimnoys  to  the 
cover  flith  wax^  Iloid  siuuki.ig  touch-paper  C  (see  §  265)';  near  the 
top  of  chimney  B.  The  smoke.  instea.l  of  rising,  as  it  usually  .loos 
rapidlj  descends  the  chimney,  and  in  a  few  seconds  will  be  found 


VENTILATION. 


165 


ascending  the  chimney  A.  How  do  you  explain  this  movement  of  the 
smolie  ?  Cover  the  orifice  of  B  with  the  hand.  What  happens  after  a 
short  time?    Why? 

The  last  experiment  furnishes  an  explanation  of  many 
familiar  phenomena.  It  explains  the  cause  of  chimney- drafts, 
and  shows  the  necessity  of  providing  a  means  of  ingress  as  well 
as  egress  of  air  to  and  from  a  confined  fire.  It  explains  the 
metliod  by  which  air  is  put  in  motion  in  winds.  It  illustrates  a 
method  often  adopted  to  ventilate  mines.  Let  tlie  interior  of 
the  tin  vessel  represent  a  mine  deep  in  the  earth,  and  the  chim- 
neys two  shafts  sunk  to  opposite  extremities  of  the  mine.  A  fire 
Ifept  burning  at  the  bottom  of  one  shaft  will  cause  a  current  of 
■■■iv  to  sweep  down  the  otiier  shaft,  and  through  the  mine,  and 
thus  keep  up  a  circulation  of  pure  air  through  the  mine. 

Liquids  and  gases  are  heated  by  convection.  (Wliy  not 
solids?)  The  heat  must  be  applied  at  tlie  bottom  of  the  body  of 
liquid  or  gas.  (Why  not  at  the  top?)  There  is  a  still  m'ore 
important  method  by  which  heat  is  diffused,  called  radiation, 
the  method,  for  example,  by  which  heat  reaches  us  from  the  sun, 
which  will  be  treated  of  in  its  proper  place,  under  the  head  of 
radiant  energy. 

§  112.  Ventilation.  —  Intimately  connected  with  the  topic 
Convection  is  the  subject  (of  vital  importance)  Ventilation, 
njasnnich  as  our  chief  moans  of  securing  the  latter  is  through  the 
agency  of  the  former.  The  chief  constituents  of  our  atmos°)here 
are  nitrogen  and  oxygen,  witli  vaiying quantities  of  water  vai)or, 
carbon  dioxide,  sometimes  called  carbonic  acid,  ammonia  gas, 
nitric-acid  vapor,  and  other  gases.  The  atmosphere  also  eon- 
tains,  in  a  state  of  suspension,  varying  quantities  of  small 
particles  of    free  carbon   in   the    form  of  smoke,   microscopic 

Oiofanisms.   and  (hist  nf    innnmoroJjln    o.ih°f'jii'>c''  \"     -'•   'I 

constituents,  except  the  first  three,  are  called  impurities.  Carbon 
dioxide  is  the  imi)urity  that  is  usually  the  most  abundant  and 
and   most   easily   detected  ;    so   it  has   come   to  be  taken  as 


>i^? 
«« 


Ht 


m 


p 


ithi. 


MOLECtTLAil  ENERGY.  —  HEAT. 


tlie    measure   of    the    imnnritv    ,.f    fi 

contams  about  4  parts  of  it  by  vohnue  ia  10  000      T    ."i  ' 

t.tv  rises  to  10  parts,  the  air  beeo.es  u'vho'lele      '"  ^^""^"■ 

in  the  water,  and  ^00^  h     „   1^"''',  ""'^"^  "^^'^  ''''  "»^^  ^'^^-Ivec 
suspended  for  a  timeTn      .  '  '    '"""  ^■'^'•"^"^t'^'  ^vluch  remains 

at  the  bottom  "  "''  ''^""''  '"*  «"^"^'  «^"1-  -  a  white  powder 

Experiment  2.    Take  a  fresh  quantity  of  lime-water  iu  eaeh  of  two 
gh^sses,  and  i„  any  i,oorly-ventilated  room  wlcl    Is 
been  occupied  by  several  persons  for  a  sho  t    in^ 
(unfortunately  almost  auy  school-room  willausw 
tJ  e  purpose),  place  one  gias.s  near  the  floor  and  w   h 
a  he  lows  blow  into  the  liquid  a  few  pufls  of  the  ow 
stratum  of  air.     Then  place  the  other  glass  near   1^ 
op  of  the  room,  and  blow  with  the  beUows  some 
the  upper  stratum  of  air  into  the  lime-water.  1      ., 
oases  carbon  dioxide  will  be  found  to  be  present 

rsho«?bv  tr"  ''""'"'^  "•  "''^  '"^'^-  ^^raium, 
as  sho«n  by   the  greater  rapidity  with   which  the 

cloudu.ess  is  produced  in  the  upper  stratum! 


Pig.  109. 


pla^>WrrToot-  ^"  "^«  ^-t'^'- «f  ^  «nmll  circular 
Plank    (J,g.   109)  insert  an  iron  wire  O0"-Mon-  and 

7-  in  diameter.     At  intervals  of  9™  sold  r  fo  t  e 

w.re   short  pieces  of  small   wire,  so  as  to  p  oleet 

hor,.outally  from  the  large  wire;  and  to  the  fr  c  e" 

trem.fes  of  these  short  wires  solder  small  cL^uIar 

platforms  spirally  around  the  vertical  wire  Fix 
stmnps  of  candles  upon  these  platforms  by  means  of 
"  l.ttlc  melted  tallow.  Light  the  candles,  and  oaref^  W 
<«>ver  the  whole  with  a  tall  ^Wass  u^     jr'^J^^ 

replaced  b7ca;bo"r;St'';r'r"  '""  '^"^  ^^''^'^''^  extracled' a'nd 
thetopot-L^r- t^U^S^;,^^^^^^  «--•  ->  --"-dates  at 


".hlch  til,- 


VENTILATION.  167 

Carbon  dioxide  is  about  one  and  one-half  times  heavier  than 
air  at  the  same  temperature  ;  consequently,  when  both  have  the 
same  temperatm-e,  and  the  former  is  very  abundant,  it  (ends 
to  settle  to  the  bottom,  as  in  the  vicinity  of  lime-kilns,  in  which 
large  quantities  of  tliis  gas  are  generated. 

The  knowledge  of  this  fact  has  led  many  to  suppose  that  a 
means  for  the  escape  of  impure  air  need  only  be  provided  near 
the  floor  of  a  room.    But  it  siiould  be  remembered  (1)  that  the 
tendency  of  carbonic-acid  gas,  unless  present  in  excessive  quan- 
tities, IS  to  diffuse  itself  equally  through  a  body  of  air ;  but  (2) 
when  it  is  heated  to  a  temperature  above  that  of  the  surroundin.r 
an-,  as  when  generated  by  flames,  or  when  it  escapes  in  the  warm 
breath  of  animals;  it,  or  rather  the  air  with  which  it   is    mixed, 
IS   lighter   than    the  surrounding   air,  and  consequently   rises! 
If  this  impure  air  could   escape  at  the  ceiling  while  fresh  air 
entered  at  the  floor  the  ventilation  would  be  good.     But  usually 
this  fresh  air  must  be  warmed ;  and   in  passing  over  a  stove, 
furnace,  or  steam  radiator,  its  temperature  will  generally  become 
higher  than  that  of  the  impure  air,  so  that  it  will  rise  above  the 
latter,  and  pass  out  at  a  ventilator  in  the  ceiling,  leaving  the 
floor  cold  ;  hence,  the  most  impure  air  is  often  found  iu\i<rh 
school-rooms  half-way  up.  " 

Experience  shows  that,  with  the  ordinary  means  of  heating, 
it  is  usually  best,  in  cold  weather,  to  provide  for  the  escape  of 
tin;  foul  air  at  the  floor  into  a  flue,  in  which  a  draft  is  maintained 
by  a  neighboring  hot  chimney-flue,  or  a  gas-burner,  while  the 
warm,  fresh  air  is  introduced  at  the  floor,  on  the  opposite  side 
of  the  room,  or  sometimes  at  the  ceilino. 

The  (luantity  of  fresh  air  introduced  must  be  great  enoucrh  to 
dilute  the  impurities  till  they  are  harmless.  An  adult  nmkes 
about  IH  respirations  per  minute,  expelling  from  his  lungs  at 
each  inspiration  about  500"'"  of  air,  over  4  oer  cent,  of  whioh  is 
carbonic  acid.  At  this  rate  about  9,000-"'  of  air  per  minute 
become  unfit  for  resniration  ;  and,  to  dilute  this  suflTiciently,  good 


!•• 


authorities  say  that  about  IQO  tii. 


-as much  fresh  air  is  needed 


168 


MOLKCULAK    ENTKRG Y.  —  H  K AT. 


?f  r, 


w 


lb  t 


Wi 


or,  for  i)roi)er  ventilation,  about  <,  cubic  mi'tar  of  fresh  air  per 
minute  is  neede.l  for  each  i>erson,  or,  in  KnglislMueasure,  2,000 
caibic  fc'L't  per  hour. 

Jf  the  heating  eouhl  be  so  arranged  us  to  keep  the  floor  prop- 
crly  warnuHl,  the  v.tiat.dair  might  puss  out  at  the  ceiling,  and 
the  quantity  of  fresh  air  entering  at  the  floor  n.ight  be  nn.eh 
less  than  that  just  stated.  I„  „,il,l  weather,  when  the  fresh  air 
does  not  require  warming,  the  inlet  may  be  at  the  floor  and  the 
outlet  at  the  ceiling. 

QUESTIONS    AND     PROBLEMS. 

1.  How  would  ya»  ventilate  the  tall  jar  in  Expeyiuieiit  3? 

2.  At  evening  assemblies,  i„  lighted  halls,  what  two  fruitful  sources 
of  carbonic  acid  are  ever  present? 

3      Why    are  gas-burners  frequently  placed  under  the  orifices  of 

\  dltllcli ■'.; ill  J 

4.     A  b.  -room  is  3'"  square  and  2.o-  high;  how  long  would  the  en- 
closed Hi;  sm  ply  two  persons  on  the  sui.position  that  none  was  to  be 

..^\^  ^f  '''""'''"'  '''  "'«""''^"^'  Per««»S'  a»tl  its  dimensions  are  3o  X 
18 X  7".  How  often  should  a  complete  change  of  air  be  eflTected  that 
It  may  not  become  vitiated? 

6.  A  silver-mine  was  situated  on  an  island  in  Lake  Superior  so  small 
that  here  was  room  for  only  one  shaft.  Can  you  suggest  a  contrivance 
by  wnclut  might  have  been  ventilated?  Apply  your  contrivance  to 
ventilate  a  tall  jar  with  no  opening  except  a  narrow  one  at  the  top,  and 
test  its  efficiency  by  burning  a  candle  at  the  bottom  of  the  jar 


XX.     EFFECTS   OF   HEAT.  -  EXPANSION. 

Havliig  learned  something  of  tlie  nature  of  heat,  and  how  it 
pjisses  from  point  to  point,  let  us  examine  the  effects  it  pro- 
duces on  bodies :  these  are  expansion  and  dumge  of  state. 
The  first  gives  a  means  of  measuring  tmiperature,  and  leads  to 
a  fuller  study  of  gases  than  we  have  yet  made.  Under  the 
second  effect  of  heat  we  study  liquefaction  and  vap  ,rizalion.    A 


EXPANSION   OF   SOLIDS. 


169 


third  effect  that  is  very  obvious,  the  chmge  of  temperature,  will 
be  found  to  depend  in  part  on  whtit  is  called  specijic  heat,  to  be 
studied  in  §  139. 


Fig.  uo. 


§113.  Expansion  of  solids,  liquids,  and  gases. —Ex- 
periment 1.  Obtain  two  short  brass  t  -one  of  a  size  that  will 
permit  it  just  to  cuter  the  bore  of  tli.  r.  Hout  the  smaller  tiil)c; 
now  try  to  push  it  within  the  other. 

Experiment  2.  Fit  stoppers  tiylitly  in  the  necks  of  two  similar  thin 
glass  flasks  (or  test-tubes),  and  through  eaeh  stopper  pass  a  glass  tulje 
about  ()0«>»  long.  The  flasks  must  be  as  nearly  alike  as  possible.  Fill 
one  flask  with  aleohol  and  the  other  with  water,  and  crowd  in  the  stop- 
pers so  as  to  force  the  liquids  in  the  tubes  a  little  way  above  the  corks. 
Set  the  two  flasks  into  a  l)asiu  of  hot  water,  and  note  that,  at  the 
instant  the  flasks  enter  the  hot  water,  the  liquids  sink  a  little  in  the 
tubes,  but  quickly  begin  to  rise,  until  perhaps 
they  reach  the  top  of  the  tubes,  and  run  over. 
Why  do  the  liquids  sink  at  first?  When  they 
begin  to  rise,  which  rises  faster?  What  do  you 
learn  from  the  experiment? 

Experiment  3.  Take  one  of  the  flasks  used  in 
the  last  experuuent,  dry  it  well  inside  and  out- 
side, invert  the  flask,  insert  the  end  of  the  tube 
in  a  bottle  of  colored  water  (Fig.  UO),  and  apply 
heat  to  the  flask.  What  happens?  What  does 
it  prove?  Remove  the  flame.  What  happens? 
Explain. 

§  114.    Coeflacients  of  expansion.  — 

There  being  generally  greater  cohesive 
force  between  the  molecules  of  solids  than 
between  the  molecules  of  liquids,  the  for- 
mer expand  less  than  tlie  latter  on  receiving  the  same  increase 
of  temperature,  and  for  the  same  reason  liquids  expand  less 
than  gases.  All  gases  expand  alike  for  equal  differences 
of  temperature,  a7ul  the  expansion  is  very  nearly  uni- 
form at  all  temperatures.  Under  uniform  pressure  the  vol- 
ume  of  any   body   of  gas  is  increased   by  ^f^   its  volume  at 


!! 


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33  WEST  MAIN  STREET 

WEBSTER,  NY.  14580 

(716)  872-4S03 


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170 


MOLECULAR  ENERGY. -— HEAT. 


the  n-ee^ng-poiui  of  water  for  every  degree  Centigrade, 
oi  j,T  for  every  degree  Fahrenheit,  its  temperature  is 
raised.  These  fractions  are  called  the  coefficients  of  expansion. 
Not  only  do  the  coefficients  of  expansion  of  liquids  and  solids 
vary  with  the  substance,  but  the  coefficient  for  the  same  sub- 
stance  varies  at  different  temperatures,  being  greater  at  high 
tnan  at  lo»,  temperatures. 

In  the  expansion  of  fluids  we  have  only  to  do  with  increase  of 
volume,  called  cubical  expansion.     In  the  expansion  of  solids 
we  have  frequent  occasion  to  speak  of  expansion  in  one  diroc' 
tion  only,  and  this  is  called  linear  expansion. 

§  lia  Power  of  expansion  and  contraction.  -The  force 
which  may  be  exerted  by  bodies  in  expanding  or  contracting  may  be 
very  great,  as  showa  by  the  following  rough  calculation:  if  aTLn 

500O  c  ?a  d^uirr^dT';;  '7f ''  '"'"  '"  ^^  ^'"''^''''^  ^-^^  «^  -<-r)  to 
500  C  (a  dull  red  heat),  its  length,  if  allowed  to  expand  freely,  win  be  in- 

l^ow,  a  f.rce  capable  of  stretching  a  bar  of  Iron  of  1  sq.  in  section 
lus  amount  is  about  90  tons,  which  represents  very  nealy  the  "0": 
Uiat  would  be  necessary  to  prevent  the  expansion  caused  by  heat  ^ 
would  require  an  equal  force  to  prevent  the  same  amount  of tntra^ 
t.on  ^caused  by  what?)  if  the  bar  is  cooled  from  600"  to  0°  C 

Boiler-plates  are  riveted  with  red-hot  rivets,  and  tires  are*  fitted  on 
carnage-wheels  when  red-hot;  why?  How  may  a  glass  stopper  suck 
fast  m  a  bottle,  be  removed  without  breaking  the  bcTttle? 

§116.  Abnorsial  expansion  and  contraction  of  water 
-Water  presents  a  partial  exception  to  the  general  rule  thai 
matter  expands  oa  receiving  heat  and  contracts  on  101!^ 
If  a  quantity  of  water  at  0°  C,   or  32°   F.,    is   heated      t 

about  39   F.,  when  its  volume  is  least,  and  therefore  it  has  its 
maximum  aensity.     If  heated  beyond  this  temperature  it  ex 
pands,  and  at  about  8°  C.  its  volume  is  the  samJ  as  at  C°.     On 
cooling,  water  reaches  its  maximum  densitv  at  4°  C     o^d  pv 
pands  as  the  temperature  falls  below  that  point.     It  is'probable' 


THERMOMElRy. 


17J 


that  crystallization,  and  consequently  expansion  (§  24),  begins 
at  4°  C.  (What  is  the  temperature  at  the  bottom  of  a  pond 
wlieu  water  begins  to  freeze  at  the  surface?) 

XXI.  THERMOMETRY. 
§  117.  Temperature  measured  by  expansion.  —  The  ef- 
fects of  expansion  by  heat  are  well  illustrated  in  the  common 
tliermometer.  As  its  temperature  rises,  both  the  glass  and  the 
mercury  expand ;  but,  as  liquids  are  more  expansible  than 
solids,  the  mercury  expands:  much  more  rapidly  than  the  glass, 
and  the  apparent  expansion  of  the  mercury _  shoion  by  its  rise  in 
the  tube,  is  the  difference  between  the  actual  increase  of  volume 
of  the  mercury  and  that  of  the  part  of  the  glass  vessel  containing 
it.  The  thermometer,  then,  primarily  indicates  changes  in  vol- 
ume; but  as  changes  of  volume  in  this  case  are  caused  by 
changes  of  temperature,  it  is  commonly  used  for  the  more 
important  purpose  of  measuring  temperature.  (Will  a  ther- 
mometer measure  quantity  of  heat  ?) 

§  118.  Construction  of  a  thermometer.  —  A  thermometer 
generally  consists  of  a  glass  tube  of  capillary  bore,  terminating 
at  one  end  in  a  bulb.  The  bulb  and  part  of  the  tube  are  filled 
with  mercury,  and  the  space  in  the  tube  above  the  mercury  is 
usually,  but  not  necessarily,  c,  vacuum.  On  the  tube,  ^r  on  a 
plate  of  metal  behind  the  tube,  is  a  scale  to  show  the  hight  of 
the  mercurial  column. 

§  119.  Standard  temperatures.  —  That  a  thermometer 
may  indicate  any  definite  temperature,  it  is  necessary  that  its 
scale  should  relate  to  some  definite  and  unchangeable  points 
of  temperature.  Fortunately  Nature  furnishes  us  with  two 
convenient  standards.  It  is  found  that  under  ordinary  at- 
mospheric pressure  ice  always  melts  at  the  same  temperature, 
called  the  meltiiig  point,  or,  more  commonly,  the  freezing  point 


■    '  ■ 


m 


172 


MOLECtTLAR  EKERGY.  —  HEAT. 


Again,  the  temperntnre  of  steam  rising  from  boiling  water  under 
the  same  pressure  is  always  the  same. 

§  120.  Graduation  of  thermometers.  —  The  bulb  of  a 
thermometer  is  first  placed  in  melting  ice,  and  allowed  to  stand 
until  the  surface  W  the  mercury  becomes  statioufi-y,  and  a  mark 
is  made  upon  the  stem  at  that  p.int,  and  indicaies  the  freezing 
point.  Then  the  instrument  is  suspended  in  steam  rising  from 
boiling  water,  so  tliat  all  but  the  very  top  of  the  column  is^in  tlie 
steam.  The  mercury  rises  in  the  ston-  until  its  temperature  be- 
comes the  same  as  that  of 


Fig.  111. 


Water  bolls . 


Blood  licnt., 


Nfax.  den.of  water 
Water  freezes 


212° 


98° 


100°., 


Abs. 
temp. 

373° 


Mereury  freezes., 


39.2° 
32°.., 


—37.8°. 


No  heat . 


—38.8° 


310° 

277° 
273° 


234.2°. 


—460°., 


the  steam,  when  it  again 
becomes    stationary,   and 
another    mark    is   placed 
upon  the  stem  to  indicate 
the   boili7}g  jwint.      Then 
the  .space  between  the  two 
points  found  is  divided  into 
a   convenient    number  of 
equal  parts  called  '    rees, 
and  the  scale  is  •        uled 
above    and    below    these 
points  as  far  as  desirable. 
Two  methods  of  division 
are  adopted  in  this  coun- 
try :  by  one,  the  space  is 
divided     into    180     equal 
parts,    and   the   result   is 
,     ^  called    t lie    Fahrenheit 

scale,  from  the  name  of  its  autlior ;  by  the  other,  the  space  is 
divided  into  100  equal  parts,  and  the  resulting  scale  is  called 
centigrade,  which  means  one  hundred  steps.  In  the  Fahrenheit 
scale,  which  is  generally  employed  for  ordiiuirv  household  pur- 
poses, the  freezing  and  boiling  points  are  marked  respectivelv 
82   and  212=.     The  0  of  this  scale  (32^  below  freezing  point), 


—273°.. 


CONVERSION  FKOM   ONE  HUALK  TO   THE   OTHER.     173 

Which  is  about  llie  lowest  tcMuiH-nitaro  that  can  be  obtained  by 
a  mixture  of  snow  and  salt,  was  incorrectly  supposed  to  be  the 
lowest  temperature  attainable.  The  centigrade  scale,  which  is 
generally  employed  by  scientists,  hm  its  freezing  and  boilina 
points  more  conveniently  marked,  respectively  0"  and  100°  A 
temperature  below  0°  in  either  scale  is  indicated  by  a  minus  si^n 
before  the  number.  Thus,  -12^  F.  indicates  12°  below  0°  (m- 
44  below  freezing-point),  according  to  the  Fahrenheit  .cale. 
Under  I.  and  C,  Fig.  Ul,  the  two  scales  are  placed  side  by 
side  so  as  to  exhilit  at  intervul»  a  comi,arative  view. 


§  121.  Conversion  from  one  soale  to  the  other.  -  Since 
100°C.  ==180°F.,.50C.  =0°F..  or  TC  .-.  ^of  rF.  Hence 
to  convert  Centigrade  degrees  into  FiUnenheit  degrees,  we  mul- 
tiply the  number  by  | ;  ,,nd  to  convi.rt  Fahrenheit  degrees  into 
Centigrade  degrees  we  multiply  by  g.  In  finding  the  tempera- 
ture  on  one  scale  that  cor.es,,onds  to  a  given  temperature  on 
the  other  scab  it  must  be  remoniberod  that  the  number  that 
expresses  the  temperature  on  a  Fahrenheit  scale  does  not,  as  it 
does  on  a  Centigrade  scale,  express  (hun.nnber  of  degrees  above 
freezing-point.  For  example,  :,r  on  a  Fahrenheit  scale  is  not 
o2   above  freezing-point,  but  u2°  — 32'  -  20°  above  it. 

Ilence,  if  you  wish  to  represent  a  >?iven  temperature  on  the 
tahrenheit  scale,  determine  the  mnnbcr  of  F.  degrees  the  jriven 
temperature  is  from  the  freezing-point,  and  then  make  allow- 
ance for  the  fact  that  the  freezing-point  is  marked  32°  on  the 
t .  scale. 


Example  1.    How  is  13°  C.  rcproHcnttMl  on  tl.c  V.  scale? 

13  C.  degrees  =  U»  X  «  =.  ^  l^.  dourees. 
Therefore,  tlic  i,nve..  temperature  1h  2Hf  K.  doKrees  above  freezing 
and  hence  is  represented  by  =- »""vi.  iieezing, 

231  -f-  32  ==  or.ii  en  the  F.  Mcalc. 


174 


MOLEC  UL  A 11   EN  E  KG  Y HEAT. 


Example  2.    How  i«  04O  R  repro.euted  on  the  Centigrade  scale? 
fi4    i.  IS  J2  F.  degrees  above  freezing. 
32  F.  degrees  =  32  X  f  =  17J  C.  degrees. 

17  J  on  the  C.  scale. 


PROBLEMS, 

Tl,e  difference  between  two  ten.peratures  is  80  Centigrade  degrees 
.  IS  the  ditterence  in  Fulireiiholt  degrees?  "threes. 

■  "2.  ,  ^:    .,^\''''"  *''^  temperature  of  a  room  falls  30  Fah- 

rclHMt  degrees,   how   many  Centigrade  degrees  is  its 
^  temperature  lowered? 

for,'  fuTr  ""  '^'"P^'-'^t"''^  «f  the  above  room,  be- 
fore tlie  fall,  was  G8°F.,  (a)  what  was  its  temperature 
after  the  fall?     (.)  What  were  the  temperaturToT  h" 

z::.^:::;"^^  ^^^^^  ^'^^  ^^"' --^^'»«  *- ^-«^-de 

4.  Express  tlie  following  temperatures  of  the  Centi- 
grade scale  in  the  Fahrenheit  scale :  100";  40°-  5fio-  ano. 
0°;  -20°;  -40";  80";   150°.  ,  ^0    ,  GO    , 

6-  Exi)ress  the  following  temperatures  of  the  Fah- 
reulieit  scale  in  the  Centigrade  scale:  212°;  32°-  90° • 
77-  20O;  loO;  _ioo,  _2oo.  _,oo.  ^qo.  SO";  329o       ' 

§  122.     Air-thermometer.  -Prepare  apparatus 

one-fourth  hter  capacity,  tightly  stopped.  Through  the 
stopper  extends  a  glass  tube  about  COo-  long,  which  also 
passes  tla-ough  the  stopper  of  a  bottle  B.^'partly  mLd 
w  ih  colored  water.  The  latter  stopper  is  j^crc  J,  by  a 
.  hole  a,  to  allow  mr  to  pass  in  and  out  freely.     A  strip 

of  paper  C,  containing  a  scale  of  equal  parts,  is  attached 
to  the  tube  by  means  of  slits  cut  in  the  paper 
Grasp  the  flasit  with  tha  palms  of  both  hands    and 
hereby  heat  the  air  in  the  flask  and  cause  it  to  expand  Tel  ICe 
through     he  liquid   in  bubbles.     When  several  buhhli   ha^  e^ 
remove  t^  hands    and  the  air,   on  cooling,  will  contr,c  ,  ^^dX 
liquid  wm  rise  and  partly  fill  the  tub^,  ^^ 


MEASUREMENTS  OF  EXTREME  TEMPERATURES.   175 

does,  i„asm„ch  aa  th^  iXht  of  L  r     ."  "■"'="'-^-*e™<"»eter 
ata,.„pbe,.i„  pressure  „tt,  I  bvZn  "  """  "  ""'"'''  "^ 

1'  r  rr  --t  "— «r^^^^^^^ 

■ng  to  the  changes  of  the  barometric  column      r„.   ■ 

scientme  investigations  a  good  air-ther™ lote;  i!   et  IJr  "^h""' 
one  conta miner   mpmnmT      t-i      *i  "J'un'ti  is  better  than 


r  F.),  and  therefore  c  It  bc^l.s  "f  ^.X:'-!""  ^•*-  '«• 
above  or  below  these  points.  K  ",',",  Wn  '""'r'-"""- 
measured  b,  the  expansion  of  .^M^T^T:,^ 
mum,  and   the  instrument  uscil  fnr  i  ,r.  ' 

Wrcm*..      Alcohol   is   ,17  „     I,         ''":"°'°  "  ™"'''  " 
measure   c.tremel,   lo     t™  „,■    u,«        IT    "  "7'"-'"'   '" 


I 


'I 


176 


MOLKCCLAK   ENERGY HEAT. 


§  124.    Absolute  temperatura       Tf    i,  j 
is  hcatci  .vhilo  tl,.  mossier,  r        ~        ^^  °'  ""•  "'  ""C. 

perat,„.a'„aL*       T\t  ''■'°.  '""'  "<■'"'■"=  «•  "«  tern- 

its  tem,e,at„  0  ,^  ,„t!  5    a„d  .r"r''  'I  "'  ""  ''™^  *«- 
continue  to  di,.i„i.„Tt:;     1'    fe  ".T-    7,?c":"  "^°  '^ 

ove.eo„,e°brrr„rt';:ert,:r  "^7^""';  -"'r- '» 

oohesioii  in  a  Tas  l|i.„  „,v      ,     ,  """'  *«  "Uromolccular 

temperature  and  nte,  "      "  "'""'"°<'  ""'^  »'  ^  '•""y  'o" 

tendency  re;panr;TV'."'"°  "  ""'^^  '°  -"'«'  -y 
tl.e    conlin- 4r  ;    '    ;  ^or"  '   "'?"  '"  "■"' '  P'™^""  "" 

Fo,-  tld,%l;o    Ij^;"'  ^'""'     ''  'owe»t  possible  .empe,.atu,.e 
tnre  reoko  "d  from  ,„  •'?•'"  *"'""'  ^'■'''  """  '™PC'- 

o..  t,ri.  sea:i„t:;:::trrjdr:„re':'^ '-~ 


w 


anasolu,.s,.tl/"efor"^h  !^^^^^^^  ^'"^^ '^ro  convcrtea  imo  liquids 

"as  never  been  cooled  to^l  o  a,  soln^!  f  ^^  ''^-     ''^"«"^'>'  '"^  ''«'>V 

-nclusive  than  tbe  one     •  v"    '  "^t^^^  arc  reason.s,  far  n.ore 

further  stu.ly  of  l.eat     he  ^^o  of  n  '  '"'^  "'^"''  --"•'°  ^'-     i»  ^"e 

great  convenience  '  ''"  ''''^'  °^  '^'''^"^"te  tenipcrature  Ls  a 


The  ab.solute  temperature  (..so.  on  the  aWe  theory)  .ay 


LAWS  Op  gaseous  bodies.  177 

Ir/r'c"'  tot/ "','"  "^ """"'  ™ "  c-"-^™"^  "-■"'-- 

Fig.  n  1  )  ^^    ^"^  ""  "  P'""'=''''eit  tbermomoter.     (See 


if 
1'i 


§  12S.    Laws  of  gaseous  bodies.— II  folloivs,  from  thn 

Cc2'r«'"'V*  "'-"f '"■'•■<>""'  ">  U,  ul>,olntete,n,eriL      Z. 
.8  called  tte  £aw  0/ C'/ian'es. 

If,  however,  a  body  of  gas  at  0"  C.  is  enclosed  in  a  vessel  of 

'  s  "tti-:  r'™' :"'  "-"^  '°"^"'»' »' "» "C"' 

il    M  '  "'  '■"'  ''«<■•■' »'»W   i"  tl,e  l.rcvions   sec 

uon,  the  pressure  on  the  sides  is  increased    l,v  ,1,  of    IL 

cunnn  shed  jfj  for  every  degree  lis  temiKrature  f.alls;  and  if  it 
were  to  continue  to  decrease  at  this  rati,  at  -27a»C  it  wolld 
become  nothing.     Hence,  >,.  pressure  „}  a  glZtiXoftu 


!f 


,!^^fc/f  n»  w,    /T  "  """""'^  /-'-"^-'-o™.;  ,0  aepressure  to 

pii-^f^'iifi  una  tlie  volume  in  mnQ/n^it      tr,  ^^      •  . 

r,f^r,o   ti  ■  7     '"""^ '*  '^^"^'^"f-     Hence,  m  a?*«  myen  mass 

o/,a«,  «,.^rod„c,  is  proportional  to  t„e  aOsolute  tel^^raZr^ 


PROBLEMS. 


178 


MOLECULAR  ENEUGY.  _  HEAT. 


% 


m  -JcV    ^''  """'  "'"  """»  """■»"  "  ■'"  temperature  become, 

temp. ,  the,,  2„3 ,  mT^'.  st^V^.     Z'        "'  '"''"  +  ''"^  '»^  ""»■ 

4-   '^""■'intvolume  vvillaliterof  cascnnfrnnt  if        ,    .. 
to  -]5o  C.  ?  ^      contract  if  cooled  from  30°  C. 

w^t::^:r;nin:;^:;:-— -  -  ati„o.p,.ero.ni  .a. 

«00«  per  square  centimeter?      '""'''-'''*"'^^'  "^^  "••^•««»'-e  i«  reduced  to 

and^nJrr;t«:frr"^^^'"'^  '^^  '^  ^^'"P^'-^'-  °^  ^^"C- 
be  its  volume^tTtemper ,  fo  270  P  ""^™''"''  '^  ''"^^"' '  ^^'^^'^  "'» 
«quare  centimeter?     S  r^  170  r  ^1 ""'"'  '  ^'"'^'^"^'^  '^^  l"^^"*^  P^'^ 

270c.  is  equivalent  to  sooot^s.^p.  ^;?::;:'S'.VorT:'^-  ''"''■ ' 

1200.     Whence  x=  344  8ce       l^^  ^ ''^»  290 :  300  :  .•  600  X  800 :  a;  x 

will  Its  volume  bo  reduced  to  l~  ,„,,,  ' '"  " '""  'e"'l'e™turo 

centimeter,    A.s.  :  ^X^'Z^X -Z^l^c    "' ^'"' -»■■  »1"»™ 

na^e/rp*%rSrb„r  '"-  -^'-"'^  ^=">°  »■  "'■'--.  -"."es 


DIFFUSION   OF  0ASE8  AND   LIQUIDS.  179 

§127.    Pressure  of  a  gas  due  to  the  kinetic  energy  of 
Its  molecules. -Consider,  then,  what  a  molecular  storm  must 
be  ragn,g  about  us,  and  how  it  n.ust  beat  against  us  and  against 
every  exposed  surface.     According  to  the  kinetic  theory  the 
pressure  of  a  gas  (or  its  expansive  power,  as  it  is  someLes 
called)  ,s  ent.rely  due  to  the  striking  of  the  molecules  against 
he  s,nfaces  on  which  the  gas  is  said  to  press,  the  impulses  fol- 
lown.g  one  another  in  such  rapid  succession  that  the  effect  pro- 
duced  cannot  be  dintinguished  from  constant  pressure.     Upon 
the  k.netic  energy  of  tiiese  blows,  and  upon  the  number  of  blows 
per  scoud   nmst  depe„<l  the  amount  of  pressure.  Hut  we  saw,  in 
§108,  that  on  the  energy  of  the  individual   molecules  depends 
that  condition  of  a  gas  calh.l  its  Wmperalure;  so,  it  is  annaren 
as  statocl  above,  tlu.t //.;>,.....  oA. ,/„«n  vian^  ;X^^^^^ 
a.s  a.  U.n,eratare.   Again,  as  at  the  san.e  tempera'tureVnT 
ber  of  blows  per  second  must  <lepend  upon  the  number  of  mole- 
cules „i  the  unit  of  spacc.it  is  apparent  that  the  pressure  of 
any  particulur  <jas  varies  as  the  density. 

The  following  estimates-  nmcio  for  hy,lro«..„  ,„ol„c«lo,s  at  0°  C    and 
under  a  pressure  of  one  atmosphere,  n.ay  pr..ve  hitercsting:-- 
Mean  velocity,  0100  feet  per  second. 
Mean  path  without  collision,  38  ten-millio„thH  of  an  inch. 
Collisions,  17,7r,0  millions  pe)        ond 
Mass,  210.000  million  milHon    li-Uon  weigh  i  ^.ram 

The  rnsiTv  !>V"'"""  '"/"""  """""  ^''  """  '='""«  ^-"^"noter. 
llie  (loiisity  of  oxygen  is   10  times  ilmt  of  hvdroiron  nt  th 

temperature  and  pressure;  what  is,  therefor  .Tic  ranv^ 

oxygen  molecules  at  0°  c,  and  under  a  pressnrc\,f  i::"::;^ 

^   §128.    Diflftision  of  gases    and    liquids.  -  The  kinetic 
theory  o   gases  explains  why  g.ses  penetnae  into  a  y  s  le 
open  to  them   and  likewise  the  phenomenon  known  as  L  \^^ 

only  de!.ty..  the  spread  of  another  gas  in    the  same  space   by 
collision  between  the    molecules  of   the  interdiffusi.-.g   gases 

'  Muxwoil, 


HI 


SH4 


180 


MOLECULAU   ENERGY.  —  HEAT. 


The  diffusion  between  liquids,  though  not  so  well  understood, 
is  undoubtedly  due  in  part  to  siniihir  molecular  motions. 


XXII. 


EFFECTS    OF    UKAT   CONTINUED. —LIQUEFACTION 
AND   VAl'OHIZATION. 


Fig.  113. 


Experiment  1.  Melt  separately  VMo^-,  hird,  and  beeswax.  When 
partially  melted  stir  well  with  a  thernionieter,  and  ascertain  the  melt- 
ing points  of  each  of  these  substances. 

Experinieut  2.  Place  a  test-tabe  (Fig.  113),  half  lllled  -.vith  ether, 
In  a  beaker  contauiing  water  at  a  temperature  of  GO"  C.  Although  the 
temperature  of  the  water  is  40°  below  its  boiling-point, 
it  very  quickly  raises  the  temperature  of  the  ether  suffi- 
ciently to  cause  it  to  boil  violently.  Introduce  a  chemical 
thermometer'  into  the  test-tube,  and  ascertain  the  boiling 
po'nt  of  ether. 

Experiment  3.    Half  All  a  glass  beaker,  of  a  liter 
capacity,  with  fragments  of  ice  or  snow,  and  set  the  beaker 
into  a  basin  of  boiling-hot  water.     Stir  the  contents  of 
the  beaker  with  a  thermometer  until  the  ice  is  all  melted, 
observing  from  time  to  time  the  temperature  of  the  contents. 

Experiment  4.  As  soon  as  the  last  piece  of  ice  disappears,  remove 
the  flask  from  the  warm  water,  wipe  the  outside,  and  place  it  over  a 
Bunsen  burner  and  heat.  Carefully  watch  the  temperature  until  the 
water  has  been  boiling  a  short  time.  What  do  you  observe?  Place 
more  burners  under  the  beaker;  the  water  boils  more  violently;  does 
the  temperature  rise? 

Experiment  5.  Place  in  contact  the  smooth,  dry  surfaces  of  two 
pieces  of  ice;  press  them  together  for  a  few  seconds;  remove  the 
pressure,  and  they  will  be  found  firmly  frozen  together.  The  ice  at  the 
surfaces  of  contact  melts  under  the  pressure,  but  when  the  pressure  is 
removed  the  liquid  instantly  freezes  and  cements  the  pieces  together. 
It  is  in  this  manner  that  snow-balls  are  formed. 

Note.  —  If  a  thermometer  is  placed  in  a  mixture  of  ice  and  water, 
and  the  mixture  is  subjected  to  great  pressure,  some  of  the  ice  will 
melt  and  the  tempcraiure  will  fall;  but  when  the  pressure  is  removed, 
a  portion  of  the  water  freezes  and  the  temperature  rises.  From  this 
we  learn  tha,t  the  melting  {orfreezing)  point  of  water  is  very  slightly  low- 

«  A  chemical  thermometer  has  Us  scale  on  the  glass  stem,  instead  of  a  metal  plate. 
BUd  IE  Otherwise  adapted  to  experimental  use. 


LIQUEFACTION  AND  VAPORIZATION. 


187 


ered  by  pressure.  The  depression  is  about  -pi-j  of  1"  C.  for  each  atmos- 
phere. Oh  the  other  haud,  it  is  found  that  substances  which,  unlike  ice- 
expand  in  melting,  have  their  melting  points  raised  by  pressure. 


Fig.  114. 


Experiment  0.  Half  fill  a  tlilu 
glass  flask  with  water.  Boil  the 
water  over  a  Bunsen  burner;  the 
steam  will  drive  the  air  from  th* 
Jlask.  Withdraw  tlie  burner,  (£uickly 
cork  the  flask  very  tightly,  ami  plunge 
the  flask  into  cold  water,  or  Invert  the 
flask  and  pour  cold  water  upon  the 
part  containing  steam,  as  in  Fig.  114. 
What  is  the  result?  Can  you  otter  any 
explanation?  Suggest  an  experiment 
to  test  your  explanation. 


If  hot  water  is  poured  upon  tho 
flask,  the  water  ceases  to  boil. 
(Why?)  Under  the  receiver  of  an 
air-pump,  water  may  be  made  to 
boil  at  any    temperature  between 

0°  and  100°  C. ;  indeed,  if  exhaustion  is  carried  far  enough, 
boiling  and  freezing  may  be  going  on  at  the  same  time.  When 
high  temperature  is  objectionable,  apparatus  is  cc->trived  for 
boiling  and  evaporating  in  a  vacuum  ;  as,  for  instance,  in  the 
vacuum- pans  used  in  sugar  refineries.  As  water  boils  more 
easily  under  diminished  pressure,  so  it  boils  with  more  difficulty 
when  the  pressure  is  increased ;  and  the  temperature  to  which 
water  may  be  raised  under  the  pressure  of  its  own  steam  is 
only  limited  by  the  strength  of  the  vessel  containing  it.  Ves> 
sels  of  this  kind  are  often  employed  to  effect  a  complete  pene- 
tration of  water  into  solid  and  hard  substances.  By  this  means 
gelatine  is  extracted  from  the  interior  of  bones.  In  tlie  boiler 
of  a  locomotive,  where  the  pressure  is  sometimes  150  lbs.  above 
the  atmosphere,  the  boiling  point  rises  to  about  180°  C 
(356°  F.) 


<i 


'  1( 


jffi, 


182 


MOLECULAR  ENERGY. -— HEAT. 


thanO°C     Fmm  fi      t  '"^'^'-'"^'^  '^  lower  temperature 

aa.,.e,  we  HZ  it  t:.-:;r'""°"'^' '-  »"-»  »'  "  »^-i'- 

LAWS  OF 
!•  ne  temperature  at  which 
solids  melt  differs  for  different  sub- 
stances,  but  is  invariable  for  the 
same  substance,  if  the  pressure  is 
constant.  Substances  solidify  nsu- 
ally  at  the  same  temperatures  as 
those  at  which  they  melt. 

2.  After  a  solid  begins  to  melt, 
the  temperature  remains  constant 
until  the  whole  is  melted. 

3,  Pressure  lowers  the  melting 
{or  solidifying)  point  of  substances 
that  expand  on  solidifying,  and 
raises  the  melting  point  of  those 
that  contract. 

4.  ^f^e  freezing  point  of  \'ater 
ts  lowered  by  the  presence  of  salts  in 
solution. 


FUSION   AND    noiLING. 

1-  The  temperature  at  which 
liquids  boil  differs  for  diferent  sub- 
stances, but  the  temperature  of  the 
■oapor  is  invariable  for  the  same 
substance  if  thepressure  is  constant. 
!  "P"'''  ''1"'fy  «<  the  same  tempera- 
tures  as  those  at  which  they  boil. 

2.  After  a  liquid  begins  to  boil 
the  temperature  remains  constant 
until  the  whole  is  vnporiztd. 

3.  Pressure  raises   the   boilinq 
point  of  all  substances. 


.  *•  ^''"'  foiling  point  of  water 
IS  raised  by  the  presence  of  salts  in 
solution. 


REFEUKNCE     TAULKS 
Melting  Points. 

Zinc 


o 
115° 


Alcohol _,,,Qo     c 

^^^rmry -;i,s  ,so 

Sulphur",  acid __.^^  ^o 

^^«  • .".'     "oo 

Phosphorus ^^ 

Sulphur.    

■^'" about  238° 

^""^^ "     -mo 

Boiling  Points  under  a  Pressure  of  ««.    A4         V 
Carbon  dioxide  . . .                           '    n    7              ''^'»^<^sphere. 
~',    ^       Carbon  bisulphide 

-1«"     pVator ."."'.'.".'.'*."."' 

''<">"     I  Mercury 


about. . . 

Silver w 

Gold .,]][     ..     "■ 

Cast-iron ..  j(,-(, 

Wr()!i,i,'ht-iron.  ..     '<  j.-i,jj_ 

Iridium  (the  most 

infusible  inetul) 

about  


42r>"C. 
1000° 
1200° 
1250'^ 
l(i00<3 


Ammonia 
Sulphur  dioxide 
I'/Uivr 


.  11)50° 

48°C 
100^"' 


which  con- 
inpeniture 
f  a  similar 


'  at  which 
[ffereni  suh- 
ttre  of  the 
the  same 
s  constant, 
le  tempera- 
"ij  hoil. 
ins  to  boil 

s  constant 
id. 

le   boiling 


of  water 
f  salts  ill 


.  100()o 
]L'()<)0 

-l2.-)(r 
JiiOOO 


48°C 


blSTILLATION. 

Boiliufj  Points  of  Water  at  Different  Pressures. 

Barometer. 

184°  F 1C.G8  inches. 

190"      18.9a      «' 

200"      23.45      " 

210°      28.74      " 

212°      29.92      " 


183 


212°  F. 
24r.5°. 
273.3° . 
30G°  . 
350.0° . 


Atmospheres. 

1 

2 

3 

6 

10 


Phe  temperature  of  the  boiling  point  of  water  varies  with  the  alti- 
tude of  places,  ,n  conse.p.ence  of  ti.e  different  atmospheric  pressure. 
Adfferenceof  altitude  of  533  ft.  causes  a  variation  of  1°F.  in  the 
boihng  point. 


Boiling  Points  of  Water  at  Different  Altitudes. 


Quito 


Above  the 
sea-level. 


Mean  hlght  of 
IJaroiueter.       Temperature. 
-.     ,„,  +9,500  ft 21.53  in 195.8°  F. 

TJt'' ''''''" ''•'"" '''° 

Mt.  Washington 6,290  "  22.90  "  200^ 

^^^•■'to" 0  "  30.       "  212° 

Dead  Sea  (below) _  1,316  «  31.50  „     ; ; ; ;  '^^^^ 

§129.   Distillation. -Apparatus  like  that  represented  in 
Fig.  115.  Figure  115  may  be 

easily  constructefl. 
The  following  ex- 
periment will  be 
found  interesting: 
and  instructive. 

Experiment.  Half 
fill  the  flask  A  with 
waf,er  colored  with  a 
few  drops  of  Ink. 
Boil  the  water,  and 
the  steam  arising  will 
escape  through  the 
nn     rn.  I    .L  ^     .  ylu^ss    delivery    tube 

BB.  Tills  tube  Is  surrounded  In  part  by  a  larger  tube  C,  called  a  con- 
denser  ^yhlch  s  kept  filled  with  cold  water  flowing  from  a  vessel  D 
through  a  siphon  S,  the  water  finally  escaping  through  the  tube  B 


■  1, 


ill 


184 


MOLECULAR    lONlOUGV.  —  mUT. 


P 


m 


The  Ptpam  Is  condensed  in  its  passaso  throni^h  fh.  ^  i- 

the  resulting  li,„ia  is  eangi.t  in  t  ^^  sS   ^^'/^'^^.'J  ^"be.  and 

colorless.     A  complete  sonlvuJu    r  „  ^'     ^''^  ^'^"id  caught  la 

HQUid  from  the  otlf     "  ^  !    ^^  ^V/^  'r;:"^^"'-^'"'"^"  °^  "^  -^^--'^ 
left  in  the  flask  A.  "^'""""^^  «'  "'«  '"^  is  effected,  the  latter  being 

The  separation  h  accompHshM  on  tho  miminl.  ih  ,  n    . 

T[:"Z :;  ;;:r 'T''^'  tt  "" '-  -'-  -'•^'-- 
o-  .1.;  ».tc.;r;::",.,r  ';:,rA  ;'---"' "■-■-'.o, 

watered  his    whiskev   ton    r..  "''''''''''    '"''«  ^''^'^ 

mistake   hv    bl  .U.0  n,i  ^      '•    '''""^^'"'     ^^    ^^"'^^^    '- 
the  result?  ^  ""'"'■^'  "^  '-^^  ^1^^"  P«'-     What  was 

which,  rising  in  bnb.h  J .    i  ,     ^  '^     '""  "^'"   ^"P^^' 

produces   a  Violent    ngita  o         ";"7/^. -— the  surface, 

place  quietly  and  .^^  .'::;;  ;''^'^:;;r^r  ^"'"^  '^''^ 

laws  of  vaporization  of  1,1  liquid  "oi;.,,''.^''''^"^  "'' 
only  the  important  case  of  water      AI  '  '""  '""  '*"'^^ 

the  evaporation  of  water  o^;* ./       ?    ''"'^'"^"'  '^^'  '^^•'^'' 
low  nvon  i.         7  *  '"'•>'  tc'nporature,  however 

low,  e\  en  ice  and  snow  evaporate. 

:rAe  rai)/(Z//^  of  evaporation  varies  dii-eeth'  ,nV/,  fho  fo 
ture   amount  of  surfree  e.pos.l,  ana  drj    Xet      T"' 
and  inversely  with  the  pressure  vpnn  tlfZui  '^'l".'"'"^^'''^'-'^' 
water  .ni.es  freely  with  the  air,  La  mnll.JXZlt 
acting  like  another  gas   (compare  §^  41  and  128V     ri 
does  not  take  up  water  Mc e  u  s  ,on<n    L 7  V'-         ^  ""'' 

f«„  ,v  *i       .  ,,*'■ '^I"*"^'' as  IS  common  y  iniao-ined  • 

for,  if  the  air  con  h    hv  rcmov..!  f.v.„,   .  .  ,  ''•sincu  , 

lar.rp  vo««ol  ^f       f  "  '^  '"*""'  ^''«''G  there  is  a 

large  Acssel  of  water,  everv  cubif  font  r.p  ^i  .      . 


Y  tube,  and 
I  caught  is 
ihe  colored 
alter  being 

•  the  tern. 
"^er.  The 
ibstancea 
operation 

ted  from 
e  alcohol 
vlio  luid 
rect  his 
fiat   was 


illj  ap- 
vapor, 
surface, 
I  called 
li  takes 
ua  and 
I  study 
y  heat, 
owever 

mpera^ 
'sphere, 
ipor  of 
ugh  it, 
he  air 
jiued ; 
B  is  a 
room 
t  does 


DEW   POINT.  jgf 

when  the  air  is  present,  _  probably  a  veiy  little  more.    In  either 
case,  on  y  a  definite  quantity  would  be  found  in  each  cubl   oot 
a  quantity  uepending  on  the  temperature  of  the  space.     Tl  u     at' 
0  C     each  cubic  foot  can  contain  0.14-  at  10°,  0.26«  ■  at  20° 
0.4     ;    and  at  30°,  0.8o«.     Evidently  the   capLi  y   i^  LL 
doubled  by  a  rise  of  10°  in  temperature.  ^ 

amLnfnf   ""7  P°^^*--When   a    space    contains   such  an 
amount  of  water-vapor,  whether  it  contains  other  ^ases  or  not 
that  Its  temperature  cannot  be  lowered  without  som^ of  he  wat'; 

^irz^^ ''' '''™  ^^  ^  "^"^^''  ^h^  «p-  ^«  -i^ : : 

in  w  .    h  :.  ,  ^"^P^^'^tuvo  ,s  called  the  deto  point.    The  form 

n  wh  ch  the  condensed  vapor  appears  is,  according  to  its  lod- 
t  on,  ce,,^  fog  or  cloud.  The  atmosphere  is  saidt  be  Z  or 
lum^d,  accordmg  as  the  diflerence  between  the  dew  pou.t  and 
the  temperature  of  the  atmosphere  is  great  or  little. 

QUESTIONS. 
J.  Why  doe,  o„r  breath  prCuco  a  cloud  to  „,„te,  and  „„.  ,„  a„m. 
a.   (a)  It  air  at  0°  is  warmed  to  20<>C     how"^!!!  i,.    i 

"Tu     f^  rr  ""™'  ™"  '-^  «<•  aThav    o  VeSLS 

3.  If  saturated  a  r  at  20^  is  blown  i.itn  n  „  n         .  clothes? 

ture  is  10^  what  will  happen?  '  ''""'  ^'"^^  *^^  ^^^P^^-" 

4.  Wliat  is  the  cause  of  the  sreneral  romnini^f    e  , 

rooms  heated  by  stoves  or  furnace"  ?  "^  ^^  '''''''''  "^  ^''  '" 

xxm.  my,  c^"NyK,.„Br.,.:  ,«■,,  totkntiat.  kkkkov,  and 

§  "2-     Heat  unite. -It  i„f,.„^„„„t|    „„,,,„,, 
q".u,t,t,v  of  hoat,  a,Kl  for  tins  purpose  „sta„.I„r„  „„it  o^™ 

jrom  (/  (o  i  c.    This  uuit  is  called  a  calorie. 


*• 


i 

Itr 


186 


Molecular  enetjgy.  —  heat. 


mi 


Let  it  be  required  to  find  the  amount  of  heat  that  disappears 
{i^xp.  6,  p.  180)  during  the  melting  of  one  kilogram  of  ice. 

Kiperiment  1.    Mix  l-^  of  water  at  0°  with  l^  at  200;  the  tempera. 

ure  of  the  mixture  becomes  lO".     Tl.e  heat  that  leave     l^of  wS 

when  .t^falls  f ro.n  20°  to  10°  i,s  J„st  capable  of  raising  1^  „f  ,vater  C 

From  this  experiment  you  learn  this  important  truth  A 
body.in  coolirn,,  gives  to  surrounding  bodies  as  much  heal  as  is  re- 
quired to  restore  its  own  temperature. 

Experiment  2-    Put  a  kilogram  of  snow  or  pounded  ice  at  0°  C 

is  meZl.  ""  "''  temperature  at  the  moment  the  snow 

Let  a"  be  the  temp.rature  thus  observed.     One  kilo-ram  of  wator 
has been  cooled  (100_0,o„ekilogramof  ice  has  been^^^^^^^ 
i-esul  u.g  k.logram  of  water  has  been  warmed  aO.   Therefore  (lor-2at 
calones  have  been  required  to  melt  one  kilogram  of  ice  ^'^^~'''^ 

Repeat  the  experiment  with  different  weights  of  water  and 
snow,  and  compare  the  results.  Taking  the  average  of  your  ex- 
penmenis,  how  many  calories  do  you  find  are  required  to  melt 
one  kilogram  of  ice?  <-"  meit 

Next,  let  it  be  required  to  find  the  amount  of  heat  that  dis- 
appears durmg  the  conversion  of  1"  of  water  into  steam. 

Experiment  2.     Place  1"  of  water  at  0°  C.  in  a  beaker  and  hont  thn 
san,e  with  a  I.msen  burner.     Note  the  tin.e  that  i  tkc^  T^^     e 

Ttl.:  r       ""•  '"  '''^'-  '^'•^^  "•^"  ^'"'^  Curing  Which  .he  ten;:.^    t 

f  the  watc  r  remauis  stationary  while  the  water  is  boiling  away     LeJ 
the  latter  time  be  a  times  the  former.  ^' 

Now,  as  tlie  water  receives  100  calories  during  the  time  it  is 
r.s,ng  from  the  freezing  to  the  boiling  point,  it  must  receive  about 
100  a  calones  durn^g  the  time  it  i..  converted  Into  steam  ;  but  Lhe 
temperature  of  the  water  is  not  changed  during  the  latt;r  oper! 


Jisappeais 
of  ice. 

le  tempera- 
^  of  water 
water  from 


ruth.      A 
it  as  is  re- 


'e  at  0°  C. 
xture  until 
t  the  snow 

of  water 
id  and  the 

100  — 2a) 


ater  and 

your  ex- 

to  melt 

hat  dis- 


heat  the 
raise  the 
iperature 
ay.    Let 


le  it  is 
e  about 
but  the 
!•  oper. 


TWO    QUKSTIONS    ANHWKHED. 


187 

Repeat  this  experiment,  and  flud  th(*  avcraire  ,.f  th..  .      u 
Experiments  made  by  ,nore  r  -uraf.-  I .  .  T  '''"'*'• 

than  the  above  give  the  following  rcHHl.H   J      *'  """'"'-^^^"^  '"e^-ds 

1.  rhe  amount  of  heat  that  disapptart,  or  «  tn»i  4n  /a 

kilogram  of  ice  is  80  calories.  '  '"  ^^'  '"'^^'''^  "/  «"'« 

2.  '^^^  <^mount  of  heat  that  disappenri,  oris  lost   i„  iu 

one  kilogram  of  ^aterir^to  steam  is^Z'^!^  '*' '^""''^^^^'^  "/ 

If  your  experiments  are  earefidiv  miidi.   •.•..!  ..* 

The  answer  to  the  first  (lucHtlon  1h    All,.*'*!     i      . 
melting  iee  is  oo„™„,e<,  i    d'^  LtL  J;; '':'*•."'.''''''"' l" 

similar  action  goo,  on,  tl,  l,ea  T.  ,  "  T"  '"'»  »'<'™  » 
™oIec„,es  .0  L.  t,.at\,.e  ^r:,::;';  .iZ  ^^fe  t 
longer  sensible,  all  except  the  sma,l  Auction  use^l  i7„  • 

afnospherio  pressnre.-  Heat,  tl.e  c,,  «  „7°t ITXf 
instances  .oos  i„„„rtant  worK,  „n.l  i.  'LX'tZXi  i^  ' 
the  energy  of  position,  or  ..otential  energy,  1  „„„?„;  „/," 
same  kmd  as  that  of  a  raised  weight  " 

doni'n.TZ-'"/'"'  '"."""^  "•"■■""""  '"  ''''-  -"<"■"'  of  work 
done  ni  both  instances  is  great,  as  shown  by  the  an.onn.  „n     . 

consumed  in  doing  the  work,  HO  eal,,rl...',rMr  '  '  ' 
being  required  in  the  lirst  instance,  and  f„'17  caiorS Ter  L  ^ 
gran,  of  water  in  the  second,  hence  It  re,,nlres  a  ™7  i',,'  to 
acqua-c  the  requisite  au.ount  of  beat,     ll  i.  fortunate  S  H 

•  Tills  fructjou  i«  libout  .tg. 


V 

J 
\ 


188 


MOLECUIAR  ENERGY HEAT. 


takes  a  large  quantity  of  beat  to  melt  ice  ;  otherwise,  on  a  sinalo 
warm  day  m  winter,  all  the  ice  and  snow  would  mdt,  creS 
mos  destructive  freshets.  The  heat  which  <Hsnppears  me  ."' 
an,l  boihng  .s  generally,  but  with  our  present  knowledge  of  ^ 
subject,  rather  objectionably,  called  latent  (hidden)  heat  Tho 
error  consists  in  calling  that  heat  which  has  ceased  to  b^  heat 
t.e. ,  has  ceased  to  be  molecular  motion.  ' 

fh  I?*:    ^^^^""^^  °f  producingr  artificial  cold.  -The  fact 
that  heat  must  be  consumed  because  work  is  done,  in  tl  e  con 
version  of  solids  into  liauids  .nd  liquid,  into  vapor  ,  an      a  I 
smple  expansion  of  gases,  is  turned  to  practicll  u^e  in  ^ny 
ways  for  (he  purpose  of  producing  artificial  cold.     They  are 
emoraced  under  three  heads,  viz. :  Cola  prodncea  hy  soLion 
by  evaporation,    and   by  expansion  of  gases.      The    followiuJ 
experiments  will  illustrate  :  —  loiiowiug 

§  135.   Cold  by  solution. -Freezing  mixtures  _  Pv«    • 
ment.    Prepare  a  mixture  of  2  parts  by  wei^hr..?  i^T  ,     '^  "" 

nium  nitrate  and  1  part  of  anuno'minV H.lS  am     hs  oh'        T'"" 
Of  water  (not  wanner  than  lOO  C).  .tirrin,  L :i:'::::t^::j::::: 

with  a  tcst-tnl,e  containing  a  little  water.' 
What  js  the  result?  What  temperature  is 
mdicated  by  a  thermometer  placed  in  the 
mixture? 


Fig.  117. 


One  of  the  most  common  freozin<r 
mixtures  consists  of  3  parts  snow  ov 
broken  ice  and  1  partof  common  salt 
The  aniuity  of  salt  for  water  causes  a 
lupiefaction  of  the  ice,  and  the  result- 
iiig  liquid  dissolves  the  salt,  both  oper- 
ations  requiring  heat. 

result?  '^"'"^'^'^  evaporates,  and  what  is  the 

Kxperiment  a.    Plaeo  water  at  al,out    10°  C.     in    a    tlm,    . 
cup,     such     as      is     usorl     in     fH^     n         ,       ,  *'""    P"''o"s 

J«    «.ed    in    the    Grove's    battery,  and    introduce 


on  a  single 
It,  creating 
in  melting 
tlge  of  the 
teat..  Tiic 
io  be  lieat, 

-Tlie  fact 
3  the  con- 
and  ill  tlie 

ill  many 
Tliey  are 

solution, 
foil 


EXPANSION  OP  GASES. 


OWIU" 


-Experi- 

eU  ainino- 
iu  ;J  parts 
llssolviiig, 
tie  water, 
erature  is 
ed  iu  the 


froezinjr 
snow  or 
ion  salt, 
causes  a 
i  result- 
tli  oper- 


he  pahn 
at  is  tlio 

porous 
trocluco 


189 

Will  so  hasten  evaporation  that  in  the  course  offl.^         ^      """  ''"'''' 
wlU  bo  a  very  sensible  fall  in  temperatr  """^  """^^  '""^'^ 

llZWUh'Z'^;/"";'""'^  ''''  •'"^'^  ''^  ^"  --^  thermometer  (Fig 

1  he  water  iu  the  stem  will  quickly  freeze  even  in  a  warm  room.  ^ 

QUESTIONS. 
I    How  dir  '''''''  *^'  ''''*^'''''  ^''^^^^'^^  ^'"»  '^l^ohol  and  wa..r  ? 

3.-  m;  dtr^r rir  r "" "  ^-^  -™^-  ^ 
the^e:prtreirL^-rrCp""^^^"^^ 

6.    How  does  sprinlcling  a  floor  cool  the  air  of  a  room  ? 

§  137.  Cold  by  expansion  of  gases.  -  When  a  beer  bottl« 

duS  ;[;fj;"«»>^  >"•«'"-<.  in  the  „..  „?.r  S 

uue  to  tne  chiil  of  an  expanding  gas 

eZnl  into  '  vl"™  ^"^  ""•■  "  ""-""^O  ""  ''  """-^  ^ 
nT^hl  ^  mt  '  "°  '"'*  •'  ''''"'=•  "»"  *<=  temperature  is 
not  changed.  What  conclusion  does  this  point  .„  conoe^n^- 
..Uern,olec„lar  .attraction  in  air?  By  allowing  condc°S,7a^ 
ont.,n,„g,  as  it  usually  does,  watery  vapor,  toLape  sudden; 
from  the  vessel  m  which  it  is  conflned,  icicles  have  been 
formed   around  the  oriBce  whence  it  escapiis. 

dissolve  more  (hot  water  will  dissolve  about  twice^irw.  „ht  "  /  tht 
substance).  Then  set  the  hot  solution  in  a  place  where  Tt  will  not  k! 
d.sto-bed,  and  let  it  stand  for  about  24  hours' tit  "t  ma  "aluirtS 

soE  Tnd  a.'';^  "'"•     ^''"'  *'^  ''^^  ''  *  thermor^rt"  th 
solution.i  and  at  the  same  time  drop  in  a  lump  of  sodium  sulphate; 

»  The  eoluUon  is  now  said  to  be  »t^er$aturated. 


m 


i\ 


ns 


V  I  If 


190 


MOLECTTLAU  ENERGY.  —  HEAT. 


soJidlflcation  Instantly  sets  in    nn«i  . 

c*».e «..  puce  i„  .H„  .e„.pe  J,  j^'t.t^;:'r  :c;;r:; 

frozen,  when  its  temperature  a»am  Wl/    Th '  7  ^  " 

the  f««.i„g  „i,t,„,  i,  ,„„^„  ,o;rt™'-.  .f"    ™P«at.ne  of 

freezing ;  the  latt^.,-  fi,„..         •     ■  '  °'  "'"  "t"''  "I'ilo 

«.e  miftarfre't;:    t  '  """'  '"'  '"""  '"  ""  f^--     ''>' 


Fig.  118. 


the  mixture  receives  heat 
is  shown  by  the  continua- 
tion  of  the  melting  and 
dissolving.     But  as   the 
temperature  of  the  water 
while  freezing   does   not 
<all,  it  must  be  that  the 
beat  which  it  surrenders 
tluring  solidification  arises 
from  the  conversion  into 
heat  of  the  potential  en- 


ergy possessed  by  the  molecules  of  the  liquid 


Jn  ttCTbegLstir  TT  "  ^"  ^^^"^«  "«•     ^hen  water 

^to  a  vessel  C  of  ^Itr^  'o '"^ t:  stLrLl  *''^  ^^"^^^  ^^^  « 
tnh«  lo  ^«.,-j„__-^  ^'     -^"*^  f'teain  that  passes  t»>i-"!..'»'  rh'* 

-.t«  «„.,u..  u  I,  „a  Je:?zr  :,iri"s  :rc:i' 


liquid  mass 

time,  what 

ange  prove? 

111(1  in  giv 
1  wlieu  the 
ious,  as  u 
raising  it. 

and  intro 

salt  freez- 

1  it  reaches 

ig  tlie  ice 
o  freeze, 
water  is 
•atiire  of 
tor  while 
r.     That 


n  water 
■  tube  B 
!|?h  the 
water, 
igb  the 

in  COQ- 


SPECIPIO  HEAT. 


191 


verted  Into  steam ;  also  ascertain  tlie  temperature  of  the  water  In  C. 
and  the  number  of  calories  which  it  has  received.     Compare  the  resul 
of  your  calculation  with  tlie  statement  in  §  132. 

For  every  kilogram  of  water  that  is  converted  into  steam, 
5.3/  of  water  (practically,  considerably  less  than  this  .inantity, 
m  consequence  of  loss  of  heat  by  radiation  and  evaporation 
from  C)  will  be  raised  from  0°  to  100°.  As  1^  requires  100 
units  of  heat  to  raise  it  to  100°,  the  5.37^  must  require  537  units 
of  heat.  But  the  steam  raises  the  water  to  its  own  temperature 
without  having  its  own  temperature  lowered.  (Whence  come 
the  537  units  of  heat  that  raise  the  temperature  of  the  water?) 

Heat  that  is  consumed  in  liquefying  solids,  and  in  vaporizinn 
hqmds,  is  always  restored  when  the  reverse  change  takes  place. 
Farmers  well  understand  that  water,  in  freezing,  gives  out  a 
great  deal  of  heat,  -at  a  low  temperature,  it  is  true,  but  still 
high  enough  to  protect  vegetables  which  freeze  only  when  con- 
siderably  colder  than  melting  ice.  The  fact  that  steam,  in 
condensing,  generates  a  large  amount  of  heat,  is  turned  to 
practical  use  in  heating  buildings  by  steam. 

XXIV.     SPECIFIC   HEAT. 

§  139.  Temperatures  of  different  substances  raised 
unequaUy  by  equal  quantities  of  heat.  -  Will  equal  quanti- 
ties of  heat  applied  to  equal  weights  of  different  substances 
raise  their  temperatures  equally  ? 

rnifoTf"?'  ^'  '^"''  ^'*y^  ^^^'  °^  '^'^'  J^^<J'  and  make  a  loose 
roU  of  ,t,  and  suspend  It  by  a  thread  in  boiling  water  for  about  five 
minutes  that  it  may  acquire  the  same  temperfture  C100oc';a/the 
water.  Remove  the  roll  from  the  hot  water,  and  immerse  it  as  nuckly 
as  possible  m  300k  of  water  atQO,  and  introduce  the  bulb  of  a    her 

IT^     ;„  uT  '''  ^^^P-'^^t^r^  of  the  water  when  it  ceases  to  rill 
which  will  be  found  to  be  about  3-  (accurately  3.30+).    The  lead  coS 
very  much  more  than  the  water  warms.     Lead  falls  ahontT^^of 
degree  an  equal  ..eight  of  water  is  warmed  "'  '^''^ 


11 


m 


192 


MOLECULAR   ENERGY.  —  HEAT. 


that  .y«a^  5u«„,,7,-,,,  ^y.  LtaZMfn     '    ;      w   '''  '^"'"'"^'" 

^snhsfances,  raise  their  tel  T  ^''"^  '""^^'''  ""^  ^^'^«^«"< 

1    ««Nc  men  temperatKres  unequally. 

these  »ub,ta„oo/f,U*  to"  4^,,;::%;  f "'™  °'  """"  "' 
alcohol.     Since  lieat  a  J.,?!?'.  "•''  ""  """=''  "^  f<"'  "'-^ 

F»-<W««  of  a  ,.nU„fJT  ^  ''"'""'''' '"  ™«  "«  '««- 

^        "'c  L/y    aunitoj   mass  of  a  suh'itntino    i°  n      • 

^^^'P'^cily  for  heai  of  that  su^iancl  '  ''  '"^'^'^  ''"'^ 

§  141.    Specific  heat  definfid  _  Tf  Jc  „ 
to  be  able  to  coinn-iro  H,n    °^°°f.^-  "  J*  '«  »  great  convenience 

heat.  The  ;:;r;: ::; ;  :;:rr„.if :::r':,  ^-"i--  '"■■ 

expresses  the  co,.,„„,,»o„'i.  L,e„  .;4;'  T:!'""   '^'"^  '^^'^" 

heat  that  raises  tl,e  water  Z.'^ZTw  tot,T°-  '"""'"^  "' 
96.70°  (from  3.3-  to  100°1  •  l,.,,!?^  *   ""'^^'  "«'  '«'<! 

3£_  to  iW  )  ,  henos,  to  m„e  the  lea,!  V  req,me» 

j,g_j_.084+  as  much  heat  as  to  raise  tlie  water  1°. 

The  specific  heat  of  all  solids  an^  K„..-i 
iocreases  slightl,  with  the  ^„1    '-rt'  '"'  "'"''  «"'"' 
hasaspeciScheatotI,.  at  W      Jo  v    >  -»  '^         "'  "°^- 
stances  i„  a  liquid  s.tj  usu^^'i^l^hi:  e     ;e  j l^tt  T 

teat  of  steam.  '""  """■"  """'  ""'""<'  the  spceiflc 


heat  that 
to   water, 

conchulo 
^  different 

inerciiry, 
i  inei-c'iiiy 
'  ia  rising 
'  each  of 
iicli  Jieat 
for  the 
ess  than 
capacity 
the  tem- 
illeil  till'. 


'eniencc 
ices  for 
'  which 

for  heat 

'  calcu- 
tity  of 
le  lead 
jquires 


gases, 
0°C. 
Sub- 
L  than 
le  the 
•ecific 


DIFFKinONCE   IN  CAPACITY   VOH    HKAT. 


KKKEUKNCK    TA1JLK8. 
Tahle  of  mean  specific  heat  htlween  i)"  (',.  and  lOO^  C. 
">'f''"«"^" ;U0!)0  I  Iron ' 

(-'opplT 


193 


Air 

Sulpliiii 
CJlas.s . . . 


.202fi 
.1770 


Mercury 
lA>tu\  .... 


.li;58 
.0!)-,2 

.();5U 


Specific  heat  of  the  same  s„hsta„ce  in  different  states. 


Water... 
Bromine. 
Lead . .  . 
Alcohol . . 


Solid. 
.0040 
.0833 
.0314 


''''l"''l-                      ClaBeoiiH. 
1-""W      4,so.-, 

•1«W     0.555 

.0(02      

•0'5-77 ■■".45 


§  142     Causes  of  difference  in  capacity  for  heat.  -  Of 
the  wholcMinanUty  of  l.cat  applied  to  a  Holi.l   or  Iic,nid  body, 
only  a  part  goes  to  increase  the  heat  of  the  body    and  thereby 
to  ra,se  its  temperature  ;  the  renKiinder  perforn.H  'interior  work  in 
overconnng  cohesion  between  the  n.olecuh,.H  of  the  body,  and  in 
fomng  them  to  take  np  new  positions.     The  greater  the  portion 
of  heat  consumed  .n  interior  work  upon  a  l,ody  the  less  there 
IS  left  to  raise  its  temperature,  and  co„He(,uentiy  th.,  greater  its 
eapacty  for   heat.      Again,  considering' tb.t'.rticfn'f  heat 
which  does  raise  the  temperature,  since  the  temperature  depends 
upon  the  average  kinetic  energy  of  each  molecule  (§§  108     109^ 
It  is  evident  that  the  quantity  of  h.at  required  to  raise  the  tem- 
perature of  a   unit  of   mass  of   a  substance    1°,    i,s   greater  the 
greater  the  number  of  mnh.cul<.s  in  a  unit  of  mass.  Thus,  much 
nioreheati,srequirnitor..,ise    .h.  t.npera.ure  of   a  pound   of 
water  1     than    t„    ,,u.se    that   of   a    pound    of    lead    1°  •     (I) 

1pT'%"7.m   ;■"'"'"■   "■"■'  '^   ''^"^  '"  '''«  water  than  in  the 
lead,  and    (2)   be<.,,use  tJ.ere  are  more   mohcnU,  in  a  pound  of 
water  than  in  a  po.nid  of  Uad.     There  are  other  matters  to  be 
considered  in  connection  .itii  the  subjec-t  of  this  paragraph,  but 
the  limits  of  this  work  forbid  tiicir  discu<«iou.  ^    ^    '  ""' 


ti 


194 


MOLECULAR  ENKRGY.  —  HEAT. 


given  ra.;o  o       ;    ;    :',  Z^  "'  T"  '"  ^'^"''"^'  ^''-"^''^  " 
The  quantity  of    ^X    at'  r  ^'^  f-  "'""'''  ^"^'^''^^  ''^'^'•^g-'- 

.»00°C.,  or  above  a  rod  heat     Co  i.  r:  kT       '"  ^  "^ 
in  coolinjr  from  100°  to  ()°r     •      ''"'^"^'  •"'  ^^^ognmi  „f  water 

gram  of  Tron  in  cooling  f-       T"  "''  ''  "^"^'''  ^'^'^^  ^^  ^  ^ilo- 
e  uuii  lu  cooling  from  about  900°  to  0°  C. 

QUESTIONS  AND  PROBLEMS 
at  Joo"c:;  '""^'  "^^^  '^  '''^''''  *«  '••-^-  100.  or'ieo  at  oo  ,„to  stea. 

boiler  at  a  temperatut  om'"  '^  J  X'.  ?  -;'!'--'tK„.  n.urus  to  the 

ins.     ih)  ri.e  same  q.mntity  oTJZl^^         ^'''"'  "'"^  '"  ^'"^  ""'•'<'- 
of  water  from  0°  to  lOo" ?  ^       ""'  ''""'^'  ^'^'^'^  '»"^v  "'",.y  kilo^a-ams 

«•  (a)  Apply  the  same  X  ;:;tl^^  J^  "-''^  "•'^".'  "  ^^^  *'>  ^"^  C-  ? 
water,  each  at  a  temperature  oTooc"^^,^*!  ''"f  7'  «"''*  of  ice  and 
boiling  point  What  Will  be  the  ten.poratur  o"  t^o^  '  T'"'"^  "" 
Will  not  both  have  the  same  temperafaT;  '""""^'^  '     ^'^  ^^"^ 

6.    What  effect  on  the  temperature  of  the  air  hn«  fh„  f       , 
water  of  lakes  and  other  bodies  of  water  ?  ''"''"^  °^  "'« 

be  Ib;:LX:m;:i::r^-^  ^^  ^^  -  --  atooc.  what  Will 

put'-intrif Of  '^:::rt^:J':z:  it'''--'  ''  ^'  '"''^^  ^*  ^««^'  -'- 

II    ™„.     "»(cr,  ato   raises  llsteinpc;atiireto6°c  ? 

9.  ;;^»^°frae'^>.ryat80<'w,:imcltwl,a.wcisl,toflocatO=L  , 

tor,  f.?e.c,S  ■',,„!"     °'"""'  ''°''  '"'""""  -"'-■■ -d  w,„. 


THEKMO-I>YNAMIC3. 


lOS 


XXV.     TnEnMO-DYNAMICS. 

M,  «,W,  ofscence  ,l,at  treats  of  tke  retation  Mween  keat  „Z 
mccUumal  t^rk.     0„o  of  tlio  most   important  discoveries 
«e„c»  ,,  tl,at  of  the  e^avalence  of,.„t  Ll  ,„rk;  thai,," 

'lf<Me  ^nantity  ,.f  fcoi;  a,„l  conver...l,j,  this  heatifL  conver- 
non  v^ere  cmpl^,  can  perform  the  original  guamUyofJ^k 

§  14a    Correlation  and  conservation  of  energy  -The 

proof  of    1,0  facts  j„st  s.Ued  was  ooe  of  the  most  toportant 

tcps  „,  the  establishment  of  the  grand  twin  conoeptfons  " 

modern  scence.     ( 1 )  That  all  l-l,,u  of  energy  are  so  relaZ  Z 

one  another  that  energy  of  any  k!ni  can  le  ckangetl  into  1^1  of 

1.NP.RGY      (2)    Tliat  wUn  one  form  of  energy  disapmars    an 

the  s,tm.  total  of  energy  ,s  nnchanged,  ~  kmwn  as  the  doctrine 
of  c„.,.„v™  o.  ..™„v.  These  two  principles  eons  1 
the  corner-stone  of  physical  science. 

iJ^*^  5°""^,'°  experiment. -The  experiment  to  ascertain 
the   .  mechanical  value  of  heat,"  as  perform«l  by  Dr.  Jonte^" 
KoK.and,  was  conducted  about  as  follows.    He  caused  a  paddle 
wheel  to  revolve  in  water  by  means  of  a  falling  weight  a[^hed 
to  a  cord  wound  aroun.l  the  a.xle  of  a  wheel.     Th!  resi^oe 
offered  by  the  w.ater  ,„the  motion  of  the  paddles  w^  t^n 
l.ywh,cl,themochanieal  motion  of  the  weight  wa.  co^vertrd 
.n to  heat   wh  ch  raised  «,o  temperature  of  the  wat^r.     Ctal 
a  body  of  a  known  weight,  e.g.,  80^  he  raised  it  a  mea^n^ 
.Lstanco,  e.5,.,  53"  high;   by  so  doing  4240'«»  of  w""    ' 

onTr^n"":"  '!;  ""'*."'"'-1-"'y  -  equivalent  amoMt^f 
energy  was  stored  np  in  it  ready  to  be  converted,  first,  into 
mechanical  motion,  then  in.»,  heat.    He  took  a  deflL  J^e^w 


€ 


!i 


'Sf^. 


196 


•11 


MOLECULAR   liNEltGY. HEAT. 


Ill 


Of   w.  er  to  be  ag.tnted,  r.g.,  2\  .t  a  temperature  of   0°  C 
^f  er  the  descent  of  the  weight,  the  water  wn.  found  to  ha  . 
Uempera  ure  of  5°  C.  ;  consequently  the  2^  of  water  must  have 
cived  10  units  of  heat  (careful  allowance  being  made  for 
all  bsses  of  heat),  which  is  the  amount  of  heat-energy  tlutt  is 
equivalent  to  4240''ff^  of  wnrV    ^7        u     ^  i  ^^ 

7,^04..".  ./•       7   ;  '        ^  '"''^  ''•^  ''^«*  *^  equivalent 

o  424  ^^  of  work  (more  accurately  423.  ySa^^"') . 

§  147    Mechanical  equivalent  of  heat. -As  a  converse 

t  e  t,:  r  ofT  'r  ^^^"^^'f -^-^  ^^^  -^-^l  --Tonment  that 
he  qua  tity  of  heat  required  to  raise  1^  of  water  from  0°  to 
O   will    If  converted  into  work,  raise  a  424^  wei-Wit  1"'  hicrh 
or  1^  weight  424"  high.     According  to  the  English  s^ltemt 

;r  Mb  W  ror^"T-  ^''^  ^--^^^/onJ  thTt\:il 
aise  ]  lb.  of  water  ]°F.  will  raise  772  lbs    1  ft    hiah      Ti,n 

lent  oj  heat,  or  Joule's  equivalent  (abbreviated,  simply  J.). 

XXVI.     STEAM  ENGINE. 

§  148.   Description  of  a  steam  engine  —  A  «f«or«  « ,  • 
i.  a  machine  i„  w„ioh  the  Castio  .Wo  o'lanATZ:: 
power       na^ueh  as  the  clastfc  force  of  rteam  is  en   reTy  d  .^ 

tlansloimcd  wto  work  or  mcclianical  motion 

The  modern  stea.n  engine  consists  essentially  of  an  arran<.e. 
raent  by  wh.eh  steam  from  a  boiler  is  eondnetil  to  botHfes 
of  a  p,ston  alternately;  and  tl.on,  having  done  its  work  in  dd 
mg   he  i^ton  to  or  ft«,  is  discharged  "from  both  sMe    a      i 
natcly,  either  n,to  the  air  or  into  a  condenser.     The  dialll 

o^^Tri  '°  '""■'"'"  '""  '-""^^  foaturetTd'" 
operation   ot    a   steam  eug  no.      T!>»   dof-^u-    -c   -i 

^cLameal  contrivances  are  purposely  omitted,  so  .■«  to  pr Zt 
the  engine  as  nearly  as  possible  in  its  simplicity. 


f 


THE  STlOAISt   ENGINE. 


197 


In  the  (lfa«n-am.  B  reprnsents  tlio  hoilrr,  F  the  furnaep,  S  the  -^team 
pipe  through  which  steam  passes  from  the  boiler  to  a  small  chamber 
VC,  called  the  valve  chest.  In  this  chamber  is  a  slide  valve  V,  which,  as 
It  is  moved  to  and  fro,  opens  and  closes  alternately  the  passa-^cs'  M 
and  N  leading  from  the  valve  chest  to  the  ojlindn-  C,  and  thus  .admits 
the  steam  alternately  each  side  of  the  piston  P.  When  one  of  these 
passages  is  open  the  other  is  always  closed.  Though  the  passage 
between  the  valve  chest  and  the  space  in  the  cylinder  on  one  side  of 


Fig.  U9. 


I 


the  piston  Is  closed,  thereby  preventing  the  entrance  of  steaui  into  this 
space,  the  passage  leading  from  the  same  space  is  open  throuoh  the 
nterior  of  the  valve  so  that  steam  can  escape  from  this  space  through 
the  exhaust  pipe  E.  Thus,  lu  the  position  of  the  valve  represented  in 
the  diagram,  the  passage  N  Is  open,  and  steam  entering  the  cylinder 
at  the  top  drivc:^  the  piston  hi  the  direction  indicated  by  the  arrow  At 
the  same  timr  the  steam  on  the  other  side  of  the  piston  escapes  through 
the  passage  M  and  the  exhaust  pipe  E.  While  the  piston  moves  to  the 
left,  the  valve  moves  to  the  right,  and  eveutuaUy  cloaca  the  passage 


,  : 


I!,  -fl! 


m 


198 


MOLECULA  ft   KNEUG V HEAT. 


N"  leading  from  the  valve  cho^f  «n  i 

and  thus  the  order  of  m^t  ZZa'  '"'  '""^^  ^  ^"^°  ^'^^  ««-«. 

the  shaft  by  means  of  ,„.  era,  k  H  t{  '^''T^'^'^^-     Connected  with 
valve  V,  so  that  as  the  shaf  ro' Ues   tl'     r""  ''""'  ''""^^^«  ^^^^  the 

sr  ^'-^  ^'^  -  oppos.t:t:;;2:  t:^  x::^  ^,  r 
- -snrr  :/t^t:;:j^  ;^^::  ^  -^e,  ..av^ ..., ...., 

serves  as  a  reservoir  of  enerffvvhr,       "'^^  '''  «i'-^»mference ;   if 
two  point,  (called  the  ^ J.  S      n  oaeJr^^T'  '.'^  ""''^  "^^  ^^^^^  P- 
the  power  communicated  direct  v  ZT  T^^""""  ^^  «>«  shaft,  where 
the  Shaft.    It  also  assists  to  make    fe  ro  n'.   ""  I'  ''''^''''''' '"  '-°v"'^' 
"jachinery  connected  with  itliform  so  H '?  "'  ?'  ^'""  ^"^  ^'"  «"-r 
city  resulting  from  sudden  el  an4   of  tl^        •'"'''"  '"""^"^^  °^  ^^J- 
aje  avoided.  (Why  should  the  wLouI tavvTx?."'^'''  "''  ''•^^^'^^^^^^^ 
Why  should  the  rim  be  heavy  ?    Se    n     02?  n^  '^^"''^  '* ""'  '^'^e' 
Ing  over  the  wheel  W  motion  nmv  h        "^    "^  ""'''"'  °^  «  '^^It  pass- 
to  any  machinery  desirable  '  ^"  communicated  from  the  shaft 

Sometimes  steam,  aftoTit  ha^  "-"n-oondensing  engines.' _ 
conducted  tbrough  t^e  elhl  2  f  ™*  "'  ""  "y'taO^'.  - 
»«*„«..,  where?  by  laL  of  '  ^  ."  '■'""""""•  <^  '""'=<'  « 
«h-oug..  a  pipe  t!  uTS™  /e  Err'rir"'' ■"'™'--' 
condensed  steam  must  be  pumpeTou  ofM  "?'"  "'"•  ""= 
special  pump  called  tecluiicalTv  tlLl  °°"*"""'  ^^  " 

vacuum  is  maintained.  Sud,  an  °  ."'T'"^-'  *us  a  partial 
er^gine.  The  adva„ta<,e  of  such  a,  *  "  °'"'"'  "  "''*"»«» 
exhaust  pipe,  instead  o  o,k  i  ,  °  t^T"."  *""'"•  '■°^'  '^  *« 
with  the  outside  air  as  in  tl  I   !  """"""^r,  communicates 

i»  obliged  to  move  ^e  pist;  rr*"™''''"^--.  «'«  ^^am 

-Wng  tau  atn,ospher  c'         ,re  :T  ""'  T'"'  "  "^'^'""« 
inch  of  the  surface  of  the  ^Z"']^  „\P""""'  '■-,«-J-  square 

-stance  arises  from  afnospherie  ::::::,T„  ^'r?' ::■  .^ 


p. 


i  M  into  the  same, 

le  piston  rod  R  to 
Counected  with 
connects  with  the 
le  to  slide  to  and 
he  motion  of  the 

vy  wheel,  luiving 
rciimferenoc ;   it 
T  the  shaft  past 
tlie  shaft,  where 
Jctiial  in  movin" 
aft  and  all  other 
hanges  of  velo- 
r  or  resistances 
•uld  it  be  large? 
of  a  belt  pass- 
from  the  shaft 


engines.'  — 
e  cylinder,  is 
r  Q  called  a 
er  introduced 
i^ater  and  the 
denser  by  a 
'US  a  partial 
a  condensmg 
Si  for,  if  the 
•mmunicates 
3,  tlie  steam 
1  resistance 
very  square 
ig  engine  no 
dth  a  given 


Uve  as  appUed 


m 


4     < 


■'■  I. ml 


i 


THK   L0(!0 MOTIVE.  jgg 

".o!ii^c^;J,^"i,^?r.^°*^^  ^-^"-  "f  the  loco- 

-u-ily  required  of  it,  fro.n  tla^e  ::  xt        r  1,         "  "k  ""''  "•^''- 
iuto  steam  per  liour.    This  is  m^comnli       ■  '""'* ''''  converteil 

a  rapid  comhustiou  of  I  Zf :;;''''  '^  ""^"-  ^■'"'  "'•'^*-  "^^ 
per  hour),    second,  by  bri ngi^     „"  'C.  ??    '  ''"  '"  "^  *«"  "^-'^l 

extent  (about  800  sq.a)  of,';  ted  ,Zt;  'r'^'^'  ^^'•"'  '^  ^^^'^^ 
A  (see  cut  ou  the  oppo.  te  pa  J   ,,  1      T  .  ^  '"  '"'^  "'  «'«  "  "''e-box  " 

powerful  draft  vviud'is  i^,  t  ■ ;,''  ;'"""  ""'^^  '^  "^^'^^^  "^  '^ 
steam,  after  it  i.as  doue  i,s  ^o;  Z  :^^:!:  ^r  =  i'"""  ^^'"^"•^' 
exhaust  pipe  C  to  the  suiolve  bov        h  '  .'  ^'  ^""''"^'^'-'^l  by  the 

The  steau.  as  it  escapes  ,Vo     tl  .  blasi  p""'  '  ""  "'"'"'  ^^'^'^^  ^^• 

and  drags  l,y  friction  the  air  „  o  '  "  ,  T''''  ^'^  "'»•  '^^>ove  it. 
vacuum  in  the  smoke  box.     Tl"  tx    '     '•  '  '''°""'''  ^  ''^'^"^^ 

then  forces  the  air  throu-h  the  fun.  ,  'T"'"'"'  ''^  "'"  atmosphere 
thus  causes  a  constant  daf.  Th  tr.  xV'";'  '7'^  '""'"^  ^'  ^"^ 
secured  as  follows:  Thewitemr  h       f,    "^^^''"^  "^  ^^^^ted  surface  is 

tact  With  the  heated  1!:^:::^/^::^  ':!::t'  ""  r^ '"  ^■"°- 

G  (a  boiler  usually  coutains  about  «^)  T  '' .""'''"""^'^  ">«  P'P^^ 
the  lieated  gases  and  smoko  Xnf  ' .  '"'' '''"""  "'"'^  ''^P^  ^»«t  by 
the  smoke  blv  and  smoke  s:^ek         ""''  '"'"^  ^"^^  "''•""«''  ^^-"  ^' 

steam  pipe  J,  etc.,  to  its  exit  ft-o  n  o  nm  k  ^  A  I"  ""''"""■^' 
neer  to  explain  from  the  object  tho  oluZl^^  huT:  t  '""''  '"^''■ 
understand.  "^  ""^'^  P"""^**  ««  you  do  not 

The  steam  engine,  with  all  its  merilH  and  with  nil  fi.    • 
•nents  whieh  .nodcrn  n.eehanieul  ur    I  a    dl^s  '       'VT"' 
exceedingly  wasteful  mnehine.     Tie  b^t tZ  t     .V"  Y  '" 


CHAPTER  IV. 

BLECTBICITT  AND  MAGNETISM 

was  to  be  i,U,o.l„cecI      So  let  ,  ,  I  f     «        '^^  ^'"  ""  """-'' 

".at  w:„  ,eaa ,.  „,„..  .^t  t'.i  :::tru:aT;;r""-'' 


I': 


i;f-: 


Fig. 120. 


XXVII.     CURRENT   ELECTRICITY. 

ami   4et        f  ^         «l'oet-zmc,  oacli  about  10-  i 
.......  and   4e."  wide;  carefully  weigh  both.     Take  also  a 

ujnbler  two-thirds  full  of  water,  and  to  it  add  about 

^tup  ,„  the  liquid.     What  do  you  observe?    Leave 
the  zinc  strip  in  the  liquid  for  a  few  minutes    tl, 
remove,  dry,  and  weigh  it.     What  do  you  find' '    '"' 

a  lifrf  "T*  *•  ,  ^'^''"  *'•"  "'^^'''  '^t'-'l'  '"  the  liquid 

Watcl,  the  surface  of  the  copper.      Now  bring  the 

"quid  intocontacr^-fE;,:''^"  "ZlTZ:!:^  '"""'T  '^^""'^ 

copper.  What  ao  .ou  obse^vop  Le^tij:::;::;::^-:  ^tS: 


CtTRRENT    ELE<;TKICITY. 


201 

CTflSr-"' "■°°-    ^"'""""■""'."'y-.weteh.hem.    What 


elea.,.     Cut  t„e  con,,:;     ;  ,    ,,"  '  T,  i,i^  '""""  "'  ~"'"'^'  "'"« 
zinc  or  copper.  ^  ''°""'  >"'  ^Parato  It  from  tlio 

wha..e„era,oo„eu,s,o„fr;::':rri;r,f:;;^^^^^^ 

It  appears  that  there  must  be  a  connection   n,„i  «   .  . 
<•  particular  kh„:,  between  the  two  ZTZ  ol    T\     ! 
may  occur.     The  connecting  wire    Ihe,    i,'  1  """^ 

m  the  eLan..es  that  nee,,,.   „    i  '  ""portant  factor 

some   iu«ueC  i     e^™  ^d  'bv    I"'  '"."""""■■''  """"""  "'-" 
tinough  the  wire  ■  in  oH  1  ^  T    ''    "'""'  """  ""«''"=' 

going°o„  in  t,::":i;.e"ic:„  :::*  ■ '"-'  ^°™"''"="  — <  '^ 

ing"rs'„1:r""'"°"  "'"  "°'^"-  ^■'^-  — >  l..-oportieM„r. 


liCjJ 


M, 


"ii'l 


™w.tea .,.  t,n.aci,an,u;;L;!i;r;.::,:;.;,,  r:';;.i!:!' ;:  ;;>■  -  «■- 

"."■  '™"'='  "I'ei,  „t  rest,  points  „„„!,  „„(,  ™t,      tT  ='"'■"• 

w,rc  helns  over  the  needle,  and  par  j  ,.  Ir  n  i  . "'°  ,™""==""s 
tremltteof  ,!,„  „,r„  „,to  contact  VI  a  'I  ',""»'  ""'  "™  <^''- 
twoext..„Utl«»orth„wi«,si  what,»r-"Lw  '        '    *""'»■■"'«"'„ 


m 


ill 


202 


ELECTRICITV  AND  MACTNETISM. 


Experiment  7.    Brine  the  ends  of  th..     , 

h  ends  of  the  .vires  together,  as  »,efore, 

Pi,  ,2,  f't^'-Po^i'iy  a  piece  Of  paper  be- 

*"-<^^'"  »'e.n.  Ls  the  needle 
moved?  Does  this  result  cor- 
respond with  tliat  of  Experi- 
ment 5?  What  ('o  the  two 
cxperiinonts  indicate? 

Experiment  8.  T  a  Ice  a 
large  iron  nail,  and  plunge  one 
end  of  it  into  iron  filings,  and 
then  remove  it.  Next,  wrap  a 
piece  of  paper  around  the  nail 
leaving  the  ends  exposed,  and 
turns  of  copper  wire,  taking  pains  that'll  ''T","  ''  ^^  '''  "'"••« 
other.     Now  connect   he  J  re  wit,  th  "T  ''"  ""*  *^^"^'^  '^'^' 

that  there  will  he  a  c„„ti„  .  1«  T       ?■      "'  ^'"^  "''''P''''"  J"***  "«^tl,  so 
through  the  coil      n  ^^^  ^T  ""^  «trip  to  the  other 

raise  the  nail.     WluU  is  t  e  1  f  "     '^""  "*'  ""  «""^"' 


«^l| 


in  acid  iy:2::j:^'':^T2r^''--''f-^-^^ 

usual     properties.       The    cause    of'  f  \  ''^'"^^*'    ""' 

allied  Phenomena  is  Xa7^r^L  ^  u"  "'^"^  ^'^- 
the  wire  are  attributed  to  th  rslte  "  .  ''"'^^  P'"!^^'^'^'-  '- 
througJi  it.  passage  of  an   electric  current 

Almost  from  the  dawn  of  the  science  of  eleetricitv  tU...  , 
been  many  who  h-ivc  bol,-n,.„i  •     ^,  t^ieciucity  tliere  ha\e 

Of  it»  existence,  and ',  er  "''  'al? 'r'^^"^  P""' 


I 


DmECTION  OF    THE  CURRENT.  ^OS 

§152  Some  deflmtions.  -  Experiments  (not  easily  per- 
formed 1^-  the  pupil)  show  that  the  eurrent  traverses  the  lia.^ 
between  the  metallic  plates  in  the  battery  at  the  same  time  tha 
It  traverses  the  eonneeting  wire,  so  that  the  eurrent  makes  a 
c-omplete  eu-c.nt  The  term  circrnt  is  applied  to  the  entire  path 
Mong  winch  eleetr.c.ty  is  supposed  to  flow,  and  the  wire  along 
h.ch  .    flows  .s  called  the  conauctor.  Bringing  the  two  extreme 

r.ll  V-""  ^T"*^^^'  ^"^  separating  them,  is  called,  tech- 

nxc^X^.maUng  and  breaking,  or  closing  and  opening,  the  circuit. 

Our  arrangement  of  acidulated  water  and  two  metals  is  called 

a  voUa^c   cell   element,  ov  pair.     A  series  of  cells,  properly  con- 

Ta^ltn'  ''  '"""^'  ^'^"^^^^  ''''  '-'-  ''  -meLe^^pHed 

§  153.   Direction  of  the  current. -It  is  evidently  neces- 
sary, m  defiuxng  a  current,  to  know  its  direction  ;  b.ft  alTo 


Fig.  122. 


Fig.  123. 


phenomena  known  serve  to  indicate  the  direction,  electricians 
have  umversally  agreed  to  assume  that  in  such  a  cell  a  desXd 
l!.o  electricity  flows /.o,.  the  copper  to  the  zinc  in  the  ^oire 

Experiment  1.     Place  the  eoncluctin^  wire  over  and  parallel  with  a 
niagnet,c    needle,   in  the  n.annor  represented  in  Fi^.   122        n^^hat 
U.rectiou  is  the  north  end  of  tl.o  needle  deflected?    Turn  the  cell  half 
way  around  so  as  to  have  the   position  In  Fig.  123.     In  wl  at  direc  fon 
is  the  north  end  now  deflected?  m  what  direction 

ofllTuatHef"  '"'"'''  *"•  ^*«"-'-''° '»-.sed  the  voltaic  pna.whlchUthep«.„, 


!5  Ji 


.    I' 


8''n  ■ 


204 


KI.EOTRrciTV  Am>   MAGNETISM. 


§  154.    Poles   or   electrodes        ti 

T-ntly  called  the  ..^a//..  ,,/,,,;,;;  Ir  ''^^'".  '"''P  ^^^  '''^■ 
;>/«^^  and  the  end  of  an/co^.'.t!^  ""f  /^''^  ^''^  ^--'^-^ 
o.-..ogative  plate  Is  called  r't  T'^  ^''''' ''^'^  ^'^I'l'^'^ 
tl.c  end  connected  wit      .0  ''J         ""■'!'''''  "'  '^'^^^"^^^^  -hile 

together  the  +  and  -  electm  /  ""^''i««"»'Ptio»,  if  we  bring 
former  to  the  lttte"acroi^^'^t''K'  "'■'""'  '""^"^  ^^^  ^h^ 
-Kl  that  electrode  s"  !  w  i^'^^^^ '  "'  °"""'^^"^  ^''-^^  I'^"^^'^ 
Pl-te  and  that  electr;;!;  is  !_"''',  "f  ?"""'"'  »""^'  ^"^'  "'^^ 
current  flows  ^vithm  the  cell  tVo.n  'Ir'^*''"'  ^"•'''^'"t  goes.     The 

cm,  tioni  the  z,„c  to  the  copper. 

§  155.  Potential  —  If  o 
one  vessel  A  to  another  B  throuT      ""■    ''''^''  ''  *'^  ^"^^  ^''^m 
-nst  be  a  greater  pressure  f  „:,  ^tl  "'  '""^  ^^^"^'  "'"-' 

at  the  other  end ;  i.e.,  iu  ordinnrv  '  '"'"  ""'^*  ^  "»''^» 

i"  A  is  higher  than  in  B  80  n ^  "?' ?^''  "'^  ^''^''  «'  ^vater 
t«-o  bodies  in  different  com  tir^^  -  ^^ 
tWcity  flows  from  one  (A)  to  "1  '''nJ'''  '^  -"-"^  of  elec- 
a  l.igl.er,,o...,,«,  than  B  '"j  'J,^"^^''  («)'-"^J  we  say  that  A  has 
+e]ectrode,  or  the  wire  connected  '''.f'T"''''  ^^^'^^^h' trioa  the 
potential  (according  to  our  .ss,m.nH  .  '  '?^^''''  '^^^^  ""  ^'^^hev 
current)  than  the  -elect  ode  "?  ''  ''''  '''''''''^^'  "^  the 

zinc.  "'""^'^^^  «'•  t^e  wire  connected  with  the 

^''^^Z:^^:^^::^;;:  ^^-  ^-^^^  ^.m  t,.  center  Of 

f-'^-  it  is  to  fill;  Whit :;  ;i  jT' '  "^.  '■""■^"■'•'  '^-^  "- 

''ij,'l't  between  the  two  J  l/l  ."''''  ''  "'"  ^^^^''^'^^^  m 
y  detennfnes  the  direction  VL^^^^^  ""'^^T''  of  potential 
electricity  that  is  to  now  thro^L  '^  '  ''"'^  '^*'  '?"^"'''^'/  of 
^--  Sometimes  th!  ot fn  f  of  f  T"/^."^-^-'  -  ^'  r;^-n 
»any  units  above  or  be  ow  that  \  .?  ^  ''  '"^'^^^^^^  '"^^  «- 
zero.  ''"'^"^   that  of   the   earth,  assumed   as 

Piaced  over  the  current,  its  deflection 


OALVAN()H(;()I»K, 


205 


Fig.  124. 


^^ 


«  the  reverse  of  that  produced  wher.  placed  beneath  it      Th- 
tends  to  conAiso  •  l)iit  ..n  .,..(:«  "«  "tneatn  it.     This 

Of  the  current  is  known,  and  to  deter- 
inn.e  the  (h'rection  of  the  current  when 
tl'-'tt  of  the  de/I  .tion  is  known.  Il" 
suggests  that  .;«  ,.„a,jine  ourselves  to  be 
swinminrj  U  the  current,  and  with  the 
current  and  faeln^  the  needle;  in  which 
case  the  north  end  of  the  needle  will 
always    he    dejler.ted    towards  our   left 

EXERCISES. 

1.  Let  the  current  be  above  the  Meedle,  u.ul  ^o  from  N  to  «?    w>.  . 
will  be  its  deflection?  **  J>  to  S;  what 

2.  Let  the  current  be  below  the  needle  ftii.l  ,,,.   r-  .    a  ^    ,r 
deflection  will  it  cause?  '         ^     '^"""  '^  *°  ^5  "'!'»' 

4-    Let  the  needle  be  below  the  current,  and  thu  deflertir  n  f 
east;  what  is  the  direction  of  tlie  current?  ^^fl^-^"^" toward  tlie 

6.   What  is  the  effect  when  the  current  In  at  the  Hide  of  the  needle? 

4^.^::::;:^:.^!^^^^^^^^      -^^  the 

and  evaporate  it,  there  wi.i  er,sta.ii.e  ou::;,::;!;;--:-^^^ 
>  G»W»noBcope.  ru^ne^^^r  Oalvani,  on.  of  tN  cw.y  .,l,..vc,ro«  ,„  ..ectricity. 


r'ul 


206 


ELKCTllUTrv   ANf)   ^rAGNETfSM. 


iri. 


^''i 


wm 


solid  ill  ucedle-lilce  crvsfAl«      ti.;        u  . 

.«.  It  exi..,  i„  „  ■„„.,„„„,  ■ ,:   '* :  't';:^:''  ,t'"- 

this   (lormanf    sf-ih.    )>,,  i    •     •  **  aioused  from 

into  mc.l,a„     u      ,;^  t"','"  "  "  '""^  ""^  "■""»f™-".«l 

by ti.e u„. .of ,,;.,; i: ''■'';,"'""""■'"''" '^ -' - •»»«- 

»=  i"  the  „,„ina,.v  h,         ;,„ T."  '":'■! '";  "•■"■°"'  '■"»  ""•■". 

-''."• "» '■■  •-»  ■'.."■ :;  "of  1':: ';  r;;:^;;. "'"" """  ^'"^'^ 

acid    ],v,l,„.„„    ,  Cm      '  f°    f '""""  '-""'  •■""'  ^"'1' ■''^ 

bubble.  „e  iz^^::i:^xry  "r,  '"^  '-""-■•  ^'^  ■■" 

As  a  plausible  but  i,.,^.flr  =X  ^  of  t""  f  "'"'"• 
the  well-known  l,yix,tl,',is  of  rJ  "''  pbeuomena 

what  ohemirt.,  1  J.vc   t  !f    ?  ""'"  °«™''-   "  "'«'"»'•'« 

«.!,...  to  outc...  into  c.„,bi„a,„/:;";;'„;,';:f  1"::- "'"" 


WHY    FIVniUXJKN    AFI'KARS. 


207 


Rg.  Iffi, 


Let  the  circles  1,  2,  3,  etc.  (Fig.  125),  represent  a  series  of 
rnolecules  of  II,SO,  connecting  the  two  phites.     At  the  instant 
the  cn-cnit  is  closed, 
the  SO4  of  molecule 
1  miiles  with  an  atom 
of  zinc,  setting   free 
its  two  atoms  of  hy- 
drogen   2H.      These 
2H  instantly  iin  i  te 
with  the  SO4  of  mole- 
cule 2,  forming  a  new 
molecule,    1',    of 
ILSO^,    and    setting 
free  the  211  of  mole- 
cule 2.       These   2H 
unite  with  the  SO,  of  molecule  3,  forming  molecule  2'.     This 
decomi)os,tion  and  re«)n)positi<m  continues  till  the  2H  of  mole- 
cjUe  6  are  sot  free.     These  211  unite  with  each  other  forming 
H,or  a  nmlecule  of  hydrogen,  which  unites  with  other  mole! 
cules  of  hydrogen,  and  finally  rises  in  a  bubble  to  the  surface  • 
so     he   molecule   <.f    l.vdrogen    that    .scapes  is  not  con.posed' 
of  the  same  atoms  of  hydrogen  that  were  first  set  free  at  the 
zmc  plate. 


m 


§160.    Electro-chemical  series.  -  If  two  phitos  of  zinc 
were  used  in  a  cell  instead  of  a  zinc  and  a  coppc..  there  >vo„ld  be 
no  difference  of  potential  between  the  two   i-httes,  an.l  so  no 
current      It  is,  therefore,  important   that  the  two  soli.ls  should 
be  acted  upon  by  the  liquid  in  different  degrees.      T/>e  qr.aWr 
the  disparity  between  the  two  solid  dements,  with  reference  t;  the 
action  of  the  liquid  onthem,  the  greater  the  difference  in  f,',te>dial  ■ 
hence,  the  greater  the  current.     In  the  folknving  electro-chemical 
series  the  substances  are  so  arranged  that  the  mostelectro-posi- 
t.ve,  or  those  most  affected  by  d.Iute  s.dplun-ic  acid,  are  at  the 
beginning,   while  those  most   electro-negative,  or    those  least 


iiiiifl 


208 


I- 
Hi 


!»>! 


ELECTRrciTY  AND  MAONHTISM. 


affected  by  tlie  acid,  are  at  the  end      Ti 

<'i-tionof  t,.cun-ent..,.o^rl;,.^:^  '"^"  ''''''''''  ''' 


Flp.  I2(!. 


'"' »"°'""  -'■«■  «  -.»lU  ,•„  the  It  leHer'"'   "■■"^- 

plate  IS  immersed  in  dilute  «„.,i  "  ™'=''  " 

Circuits,  and  a  transfer  of  ere    ,"  I'""™"  ™""'^ 
will  take  niace      Thi.  „   "7"' "'"J' "lojig;  the  snrface 

tween  the  .  ,e  ami  the        "°  ■"■'""■•  "'  ''  ""■"■  •">- 

diverts  so  „n,ehZ,;r;;.''2t°"'''™*-- 

«-ei.y  weakens  it.     r„  adjitt,  tottl!  Tr'' "" 
a  great  waste  of  chemie,!.  1  '      "'■'-"sions 

circnit  is  broken     1,1^'  "'  "'"'"  ""=  «S"lar 

eontinnes.     If  ".'n     :?:r'  '""^"'  "^  ''  «  «'"cd.  -'till 

-™  at  any  tl',:  '       Xe" TlnW  •,;'"  '°""'  -«""  "''""' 
choraieals,  except  at  times    vhel  ""  «'"»™l'"''"  of 

■"crenryisrnlJdovertrsn  ™„Jh  ""■""  "  '"""■"■  " 
'■»"  hce..  dipped  in  add  to  cle  r-.  I  """'  '"*'''  "'-  '""" 
"Olvcs  a  portion  of  te^,,  °1*.  ™'-"--  "'"  n.erenrj.  dis- 
amalgam  whieh  coverri        '  "«'   "'"'    '''   "   «<""i-li'l.ml 

-no  thea  con,por.«  itoe  I'^k   pZX"'  """  "'"  ""■"l«»"'ateU 


VARIOUS    BATTERIES. 


209 


XXVIII.     VARIOUS    BATTERIES. 
§  162.   Polarization  of  plates  _  Whn.,  4.u      • 
per  elements  are  first  plaeedia  the  dilt    ^  ''"'  '"^  ""P" 

current  of  electricity  is  iroducei     but  tho       ''1'  "  ^'"'^  ^^^^^^ 
fppl.lA      'PK  •     ^  """^^^ '  ^ut  the  current  soon  becomes 

feeble      The  cause  is  easily  discovered.     The  liberated  hZ 

visibly  covered  with  bnhhin.      ,  .  ,  '^'^^''^^^^^  P'^te  is  very  soon 

:rs„rr::  :a:  r::;r 'if-  f 

coated  with  h,d,.„ge„  Bmore.tro  ^IvZ,  !'-p„^  h':!'  "  ""? 


Fig.  127. 


^.o,.o/^7,«^,to,,.     Very  many  methods  have 
,^  been  devised  lor  remedying  these  evils.   Thov 
are  all  included  in  two  classes:   mechanic^ 
and  chemical  methods. 


tJvff'  ^"Jt^.b^*^^'^--'^^^  Smee  bat. 
te^y  (Fig.  127)  IS  an  example  of  the  former 

eass.  A  silver  plate,  or  sometimes  a  lend 
P  ate  IS  coated  with  a  fine,  powdery  deposit 
of  platmum,  which  gives  the  surface  a  rouo-h 

readily  adhere  to  it    'DHu'to    '^'''•'    ''"    ''''''''^'''   ^^'^^    -^ 
forv      Th       1  !  ^  sulphuric  acid  is  used  in  this  bat- 

th..  „eoess,t„te,  a  c„,.ta„t  ,„,.,,  to  U^  >^e  ^^TL,^ 


if 


1 


i 


210 


I     I 
I 


ELECTRICITY  AND  MA(;NETIsM. 


No  mechanical   method   can  w)mii,. 

Mrogen  on  the  electro  nc'tivo^^^^^^^  ""  '''''''''''  ^' 

Pletely  accomplished  by  Ssll  J  .   "•  ""  "^'^'  ^^^  -«- 

hydrogen,  as  soon  as  1  be  /  ^  ^      "'      '""'''"'  ''''^'  ^^^'^^  t^« 
on  as  iibeiated,  may  go  into  combination. 


Fig.  128. 


§  164.  Grenet  battery.  _i„  the 
C.reuet  or  bottle  battery  the  hydrogen 
-  ^Lsposed  of  by  chemicaf  action. 
1  he  chemical  action  is  quite  complex, 
and  will  therefore  be  omitted.     The 

'qtnd  used  is  a  mixture  of  potassium 
l^iehromate  and   sulphuric  acid  dis- 
solved  in  water.     The  zinc  plate  Z 
(J^ig.  128)  is  suspended  between  two 
carbon  plates,  C,  C.     The   carbons 
remam  in   the  liquid  all  the   time. 
(Carbon    is    now    largely    used    in 
X7r'    ^'''    "''    *^l««^'-«-"egative 

This  battery  gives  a  very  energetic  — 

only  to  ,„.a„  the  .i„o  o„t  of  ^l,o  ta  „"  , '" ,™'''  ""  ""^ 
«nd,  „„  pushing  ,h.  zinc  back  i  to  t  L,^  "l "'™'  "™  "• 
immediately.     It  is  well  u,  „l  „     .       .^      ' '""'°"  '"""menws 

-nallybylithdra„i:r,ht.tL  'uh  r^','?  "  "''"  "«""- 
With  ODB  Grenet  cell  Lriv  ""'  '^''  "  »''»'■'  'im"- 

».I,  bt.es^r™';Xttr'^   batteries.  -  There    is, 
Mia  batteries.     T|  c  ic  fs    2''""'V'.  '"'■'■""  """""■■■•  "'  '«">- 

imposed  by  it,  wi.il  ^  „•  irV",,'';"  "^:"  ^  ^  "■'■ 

and  the  condn.ti„„  ,,,.,tp  ,,  '"='1""''^  ■»  dil„te  sulphuric  acid, 

be  decomposed  b;i;ro„,'Z'''  "''  T"'  "  '""""  '"-■"  »" 
J  nydrogeu.     1  |,e  t„o  liquids  arc  usually  eep- 


IS, 


^BtmSEN's  AND  GEOVE's  BATTEEIES.  211 

arated  by  a  poroiis  partition  of  niurla,.,,!  r.,-A„ 

'<'•<■  l-vent  t„o  pa.s,age  of  4^4 '«  o  co'fri  t^''^  T 
l«Uoo-  (Fig.  129)  i,a.,  a  bar  of  ca,bo„  mZtau!'J  ""f" 
a™l  contained  in  a  porons  cup.  This  I  Z  "l'^  T"° 
"Hotber  vessel  containing  the  dilute  ,  ,1  Zr     td-'^-'" 

;;:;r„:':.r  ^•™°  'rv "  '■■"'"-  '^■'' '-'^^^^^^^^^^^^  ti;:: 

"Inch  „ea  ly  sniTounds  the  porous  cup.     The  by.lrogen  tr.v 
■ses,  by  decomp„.si,i„„  and  reco„,positi„„,  the  s,  IplXl     acH 

::;'":"'"™'Sl'''-P-™"»l.ar.itio„,andin,„ediatly      te^^^^^^^^^ 
oheunea.  act.on  with  the  nitric  acid,  so  that  nono',t;,::'l" 

carbon.         Thcrp    nm    ,...^  i       ^    i 
^ndi,    aie    prodiieetl    by 

this  action,  water  — which  in  time  di- 
lutes    the  acid  -unci  orange-colored 
fumes  of  nitric  oxide,  whicli  rise  Irom 
tlic  battery.     These   fumes   are  very 
offensive,   corrosive,   and   poisonous. 
I-    the  nitric   acid    is    first   saturated 
witli  nitrate  of  ammonium,  tlie   acici 
will  hist  longer  without  dihition,  and 
tlie   fumes   are    ulmost   entirely   pre- 
vented.     Strong  sulpluiric   acid  will 
not  answer  in  an3-  battery.     Usually, 

j;;..-.  by  «ig,,t  or  .0  by  ZZ  7::^^^,;^^ i!: 
Grove  T.sed  a  strip  of  platinum  instead  of  tlie  onrl^on  m  i  ' 

Mmmm 


iji 


rill 


I 


.jlil 


212 


ELECTiaciTr  AXD   MAGNETISM. 


FiK.  130. 


§  166.   Gravity  battery.  —  rii..  l,..+f  •     • 

this  country  for  toiog,..phiL  is  cabled    ,7  ''''"'''"^'  "^"'  '" 
copper   plate    V,    ImThmv    1°o     is  ^''"'"'^  ^"''^"^Z-     A 

placed  ou  tl.e  l,ott(.ni  oi  a  vessel 
and  covered  with  crvstals  of  cop- 
per  sulphate    (hh.e    vitriol),    and  > 
tlio    whole    covered    witli    water 
As   the   vitriol  dissolves,  its  s,,e- 
c.fic  gras-ity  causes    it  to  reuiaiu 

at  the  bottom,  iu  contact  with  the 

copper  plate.      The  zinc  plate  Z 

18  suspended    in   the   clear   li^jnid 

above.   To  start  the  action  quickly 

a  teaspoonful  of  common  salt  or 

o.  zinc  sulphate  is  dissolved  in  the 

^vater.      As   the    cheniical  action 

P'-oceeds,    the    vitriol    is     decom- 

rosed,  its  sulphuric  acid  constitu-  

p-e.  The.incd::;^--;;j::^^ 

the  electr'odes'of  ?|,f  ^o;  Gr^'::^T-  ''     "'''■"'•"•«   ""''^'-^^^^ 

S;;;--. -out ...,.,,-!-- a. ^^^ 

..^LSr'""^'""  ^'  ^"^'-^^  ^^'^  P^-^  -   the  above 


LUMINOUS    ElfVKCT. 


213 


§  168.   Luminous  effect.  -^W..  h„vo  ..i.     i 

"•      vvc  nave  nlrcady  seen  one  illus- 

^i«-i3i.  tmtion   of  tliis  ofTeet 

in  the  glowing  of  the 
white-hot  platinum 
wire. 

Experiment.  Attarh 

otic  polo   of   tlu!    hattrly 

to  a  flic  (Fijr.  132),  aiitl 
pass  the  other  pole  over 
its  roii^rli  surface.  Tlie 
/11(!  forms  part  of  the 
circuit;  and  as  the  wire 
passes  over  it,  the  (;ir- 
ciiit  Is  rapklly  inailc  and 

causes  a  spark  at  the  pouit  where  the  elrmit  ll"i,?","'  """U''"''  '''"^'^ 
Of  sparks  that  flies  fron.  the  flie  l^du^  1.!  rl:,;;.;;  '''"     '''''  •'^'""^" 

particles  of  Iron   tliat  ^'^>^-  '•''•''• 

are  pn.Jecttul  Into  llie 

air. 


Fig.  132. 


§  169,   Chemical 


effect.      Kx|M«ii. 

mcnt  I.  Kt(!cp  Home 
,  .,      .    ,  leaves   of   jiiirple   cah- 

bap;  the  infusion  lias  a  deep  purple  ,.,|or.  i,is. 
solve  a  llttie  caustic  soda,  and  pour  u  f<.w  drops 
ot  the  solution  into  a  iiortlon  of  flw.  ii.c.wi,  .,        i  ., 

tery-wires  two  narrow  strips  of    plaU,,.,,.,    ami    „l-  re  o,u    o     n 
strips  iu  each  branch  of  the  t.-he,  a  Ilt,le  way        rt    '    fh      H 
wm  be  obliged  to  traverse  a  part  of  thl  ^  ll  f' n,^  M^'^S: 
bubbles  of  gas  arctaeUlatcI^dlHcngagcafioiu  the  i-lltlnl  ^Ir^s  j 


II 

f. 


214 


ELECTEICITY  AND  MAGNETISM. 


«">Phate  Has  ta.eu  Place;  -  aeiurrari^XT^;  -J^J^  -"'- 

or  fusion.     A  largo  m,mtr  of  itf       '"'  "'"'"  "^  "<""«"" 
sodium  8„lptote,  Sf  an  acid   a,  ,1  ">f "'"''  "'''  ""'"P''^'"',  like 

™bsta„oo t„at will ,„;: ; ::'„  r";"'f r  "-'^ ''"■^■■ 

neutralize  an  aeid  is  enll.,1  .,  ;  ,       •*  ""''«'«'■«'=  *at  will 

-1  a  base   i.  called  T^^  Xk.        "  T""'°"""  °'  ™  -"< 

I'latlnum  „„  which  eo,„.cr  has  ,o  .       1+.';"'""""''    """•.  ™""ect  the 

per  sulphate  (CnSO.)  wl,  o  ,  ,'  ",'^°'7  "  ""'^  '""'eeule  of  eop- 
-conn.,  for  the  ^t^UZZ  Tt"!  "',  '""  "•■"*■•  ■''"- 
does  not  lose  its  stronoth   foTl  I         ^'""'-      '^''"=  ^°''"»" 

»;pha.e  i^  decomposed,'!    er/wr  If"'"  "?««- 
poles  are  used,  the  SO,  docs  „n,  „      i  .  '""'  Plat'iun, 

«.ters  into  chemical  .a  tt   w  t    th  "w'lT  '""n""  '"■■'""™'  ""' 
with  the  hydrogen  of  the  «^r   r  ^^'°  ^<  "'""Wncs 

o..genof  theUr  ^::::::-';^Tiotu:^-:; 


le  that  around 
'f  the  sodium 
3sults. 

»-  in  the  bat- 
battery.     A 

is  called  an 

lyte  must  be 
by  solution 

fiposod,  like 
some  other 

ce  that  will 
of  an  acid 

'olyzed,   the 

the  -j-pole. 

iilphate,  and 
collects  on 
connect  the 
ire,  and  the 
in  the  solu- 
e  the  result 

a  copper 

atom  of 
e  of  cop- 
'r.     This 

solution 
f  copper 
platinum 
mm,  but 
ombines 

and  the 
^  +  0.) 


CHEM1(;al   effect. 


215 


The  liberation  of  the  oxyoe„  is  t|,n  m^uU  ^f 

eal  action,  subsequent  to' the  clecLi;;::!!!^"^"^^^  ^'--^- 

I'^loctrolyze  this  salt  i„  sl^n'uu^Z-'''''''-     ^''  ^  '^"'^'  ^^'^'^- 
..•outh   of  tin   crystals  .1,1   slu.:    Z^^^l^''-      ^  '-^'^"I 

In  a  Similar  manner,  silver  and  1.^ 

from  then- salts,  silver  nitratl  and 
k'a.1  acetate.     Each  metal  has  its 

own  peculiar  form  of  growth;  and 
sometin,es  the   same   metal,  par- 
t'C't.larly  silver,  exhibits  different 
forms,  according  to  the  stren-th 
ot  the  solution  an,l  tlie  powc.'of 
tlic  current.      lu  Fjo-,,,.^   j.^^  ^ 
;;q)i'osents  a  silver  tree  deposited 
*'om   a  weak    solution   of  silver 
•"trate,  and  B  a  tree  fornu-d  from 
:i  still    weaker    solution    of    the 
same. 

Kxperlment*.  Re.nove  the  bot- 
tom  of  a  glass  bottle  having?  a  wide 
"•outh  flt  a  cork  to  the  n.onth.  and 
waterproof  substance  such  as  .uftTl  T  "7'''''  '""^"'att^d  with  son.e 
"atln,.  l„  piatinun.  strl^.  Fit  '"'  FUl';  T'''  ""  ''''•'''  *«""'- 
the  inverted  bottle  witldil.uc",  In  „nr-  "'°  ''''•'''''''  '^'"l  Part  of 
the  platinum  poles.  '  a  'e  1 1  .f  h  '•'"''."'"'  ''''''''  '^'  t"^^««  over 
"f  gas  innuediately  ar  e  f  ^.n  t.  "T""  "*'  ""  '^'^"^^>'-  ^^''^les 
'»  the  tubes.  About  ;wlcermcV:^^  I^n  '^'^^'^^^  "'«  "^"^^» 
as  over  the  +pole.     Thrust  •,  L,TT  ,^  "''''*''   °''^*''  "'«  -pole 

the  former  i.,  the 1 1  .a^^  ^f '';:^'-;"n  T' ^^  "''^  ^^^^«' 
rapidly  than  it  burned  in  the  a^r  Tl  ,Vi  T  '""""  ""'^"  '"«••« 
I'yUrogen  gas  and  the  latter  o  vgen  .  Tif "  .'""'  *'^'  '"""^•' '« 
"e  used  in  making  this  experin  en  '''  '^""•'  '^"^  ""^''^^  to 


21G 


KLECTUrciTV  AND  MACiNETrSM. 


Fig.  ,3..         clcsolv  lik-e  tint  Xo    r  '''*'^"  •«  ^^^n- 

.    '"^»-  uiat  already  ff  veil   fSt^o\   <. 
.'iction  iirti.e  simple  cell      T.         ,       ^   ^'"'  *'^^ 

tf"it   wat,.r   is    ultiunteh     1  ''  '^''■^^^'" 

-Ipluu-io  acid  is  o         V,  !'^^7"P«'-^''    for   no 

t"'^t  -tor  is  eon,  oil  oM       "''"'^""  ^''«^^« 
or   l.vd.o.en   to  on  .         /7  ^'"'"*^  ''J  volume 
.      u„Ln    lo  one   pjiit  of   oxvo-pn         tin 

^"•gl^t  not  copper  poles  to  be  used   ^  f^^'f  ^^ 

PO--  wi.ati:t'rrii:r^"'"^^"^-p^- 

!""1--  tia.  poles.       The  serous  iluid   t    '     o  r    '""  ''^f^'^^"' 

'eles  under  the  positive  pole  is  ad       I      T-7   ^'"''''   '^'^  ^^^«- 
"""- the  negative  pole  is  alkaline  '""  '^  ^'"   ^--^- 

tongue  „,ay  forn,  part  „f  ,1,0  ci,4m  '"'^'^'  "^'"'  '^^  "^^t  the 

Panied  by  a  peculiar  acrid  taste. 

When  a  battery  is  knowu  not 
to  be  very  powerful,  the  tongue 
sorves  as  a  very  eonvenient  gal- 
vnnoseope,  to  determine  whether 

tl'c  circuit  is  in  Making  eondition, 

'ind  approximately  the  strength  of 

tne  e.„Tent.     If  the  erural  nerve 

(n  white  cord  next  the  backbone) 

,     '''  ^'""S,  '-^"^^"tly  killed,  is  laid  '  .| 

i-tautly  eouvui!;  ^^^^^  iT  d"^'  ^^^'^'  '^  ^^^^^  ^ 

ie„  (11  awn  up,  as  represeuted  by  the 


itor  of  eloc- 
iion  is  verv 
58)   for  trie 
•"■ic  acid  is 
^O^;    then 
'  is  certain 
2(1  >    for  no 
ysis  shows 
1>J  volume 
n.       Why 
this  exper- 
"g  copper 

ne  apph'ed 

I's  appear 

the  v<is- 

'   vesicles 


3e  the  tip 
'  that  the 


MAGNETIC  EFFECT. 


tonch- 
les  are 
by  the 


217 

'lotted  lines  in  Fi"'in-p  nr.      ti, 

-ta„e  .,,0  ci,.c„ir  is  b,t  0,,™ ,  T„:,r:"'r "™'-'  ■"*= 

pieco  of  zinc   •md  tli,.  m.,    i       ■.;      '  """"S  '"»  norvo  «•  th  a 

it  ...ay  ,.o,„ai„'fo,'  J^'     1^^™  t'"'  '■"  -'  r'  '"""""■"""■'■• 
is  armed  with  a  ,„f,    .,  '  '  '"'"'  '■'""'^^-     "  one  iwie 

l«.'k  of  lh„  „„.,,-,  „,,,„;.. '',"'"'•    '■"  <>l«.-  .^  appli«l  at  tho 

--'  -'  oa.,.;  s.:ii:':;.r;f  ™:i:ir '-  '"= 

tlio  circuit;  wl,„t  lakes  pltL'-V"'"  "'""    ".""t 

of  H.l»  experiment  „,t,«,"f<°"''""'"  '""  '■""'" 
Whv  wo«  fi.„  ..  -I  exponment  8,  S  ir>l 

-I'^Cl^r  W^'r^^f  :;r'--^  P^Porin  th^^ 

--PP-'  in  pap   '    If  th  "  ;,,r      '"  ""^  ""^'  ""' 
paper,  wo„iaitUeiJ^^/l:r""^^^^^^ 


OM.th„.acertain  limit,  themorepower- 
in  y  .s  It  niagnetized.     This  arran..en  ent    . 
called  an  electro.nagnet,  becanse  itis  "  m  J 
net  produced  by  electricity.     The  ro    of  T^" 
IS  called  its  cor,,  and  tho  coil     f  ""^ 

'  ttio  coil  of  wire  the  helix.  -^ 

lusulatod,   covereil  ./..•// 


'  I. 


i 


218 


ELECTRICITY   AND   MAGNETISM. 


! 


I- 


In  order  to  tako  advantage  of  the  attraction  of  both  ends  or 

poles  of  the  magnet,  the  rod  is  most  frequently  bent  in  a  U-shape 

(A,  Fig.  13H),  :i,jd  then  it  is  ^j^  ^3^ 

called    a    horse-shoe    magnet. 

Sometimes  two  iron  rods  are 

used,  connected  by  a  rectan-        ,_  ^^ 

gular  piece  of   iron,  as  a,  in    ^H  ^H^  B       MB 

IJ  of  Figure  t38.    The  metiiod 

of  winding  is  such  that  if  the  iron  core  of  t!ie  horse-shoe  wero 

straightened,  or  the  two  spools  were   placed   together,  end  to 

end,   one  would   r.ppear   as  a  continuation   of  the   other.      A 

piece  of  soft  iron,  6,  placed  across  tlie  ends,  and  attracted  by 

them,  is  called  an  armature.     The  piece  of  iron  a  is  called  a 

back  armature. 

XXX.     ELECTRICAL    MEASUREMENTS. 

The  wonderful  developments  of  electric  1  science  in  recent 
years  are  almost  wholly  due  to  a  l)etter  uiulerstanding  of  what 
electrical  measurements  can  and  ought  to  be  made,  and  how  to 
make  thera.  Most  of  this  increased  knowledge  has  been  gained 
since  the  first  Atlantic  cable  failed  in  1858.  Let  us  learn  how 
to  make  some  of  them. 

§  172.  Strength  of  current.  — It  is  evident  that  the  ther- 
mal and  luminous  effects  of  electrical  discharges,  electro-chemi- 
cal decomposition,  the  deflection  of  the  magnetic  needle,  the 
magnetization  of  iron,  and  even  physiological  effects,  or  any 
external  manifestation,  may  be  employed  to  detect  the  presenc-e 
of  an  electric  current,  in  a  circuit  however  extended.  Since 
the  magnitude  of  any  effect  varies  as  its  cause,  it  is  also 
obvious  that  the  magnitxule  of  these  effects  may  serve  to  measure 
the  strength  of  the  current.  Now,  as  the  quantity  of  water  that 
passes  through  a  given  pipe  in  a  minute  or  an  hour  indicates 
the  strength  of  the  current,  so  by  the  strength  of  an  electric  cur- 
rent is  meant  the  quantity  of  electricity  that  passes  through  an 
electrical  conductor  in  a  unit  of  time. 


>oth  ends  or 
in  a  U-shap« 


GALVANOMKTKIt. 


219 


ie-shoo  were 
her,  end  to 

other.  A 
attracted  by 

is  called  a 


e  in  recent 
ng  of  what 
md  how  to 
)een  gained 
learn  how 


t  the  thor- 
citro-cheini- 
ncedlo,  the 
its,  or  any 
le  presence 
ed.  Since 
it  is  also 
to  measure 
water  that 
r  indicates 
lectric  cur- 
hrough  an 


§  173.  Voltameter.  _  The  quantity  of  electricity  that  passes 
any  cross  section  of  any  conduct.>r  in  the  Harnc  cinunt,  1  owe" 
U>ng   .,  unless  there  is  a  leakage  at  so.ne  point,  neces's  ri^    h 

part  of  U,e  cncuit,  and  measure  the  strength  of  a  current  by  the 
temperature  to  which  the  wire  is  raised ;  or  we  mav T.V 
water  and  collect  the  gases  resulting  theroLm /^  '^^SZ 

oj  time.     The  lattc-r  ar.angement,  called  a  voltameter,  is  easily 

Fiff.  139.  constructed  sufllcientb-  u..Mn-ate  for  many  pur- 

poses,  and  should  be  constructed  and  used  by 

•?very  pupil.  '' 

In  Figure,  m,  a  Is  a  «,a„„  ♦,,„,,  ,ocn.  j^ng  and  3=™  ia 
diameter  (a  ...uch  .short^-r  tube-  will  answer;  for  X 
ample.,  a  largo  sized  tost-tuho),  cloHod  at  one  end 
and   graduated  i.  cubic  centimeters  (this  may     o 
cloncby  means  of  a  paper  scale  pasted  on  one  side 
of  he  tube) ;  Ms  a  bottomlcHs  glass  b<,ttle  of  al)„ub 
Iter  capacity.    Through  the  Ht<„>per  of  the  bottlo 
pass  two  wu-es,  msuluted  with  gutta-porchU  or  seal- 
»g  wax,  terminating  in  platinum  .strips,  which  are 
■"•<xh.ced  a  Uttle  way  into  the  ,ube.  '  The  tube    s 
«1  ed  NM  h  water  .slightly  aclduhUod  with  sulphuric 
acid,  and  Its  oriflce  is  Immersed  in  the  same  kind 
of  li.iuid,  which  partly  IIIIh  the  bottle.     When  the 
colls  in  series  a  IH-^^T  '""'  '''"'"i'^;^'^  ^»"'  >*  'x^ttc-ry  of  two  or  more 

§174.  Galvanometer.- The  i„8tn,ment  In  mo»t  common 

besides  ,ta  ordmary  use  a,  a  gulmno^o,,,,,  ,,„rr„rn„  t  ,e  stil 
more  unpoi-tout  offlee  of  a  g,.ha,^u,-r.    Tl,'  ,i„,p|„  ...a^ne  " 
r.e.dle,  used  as  ah-eady  described,  answer,  lolcraby  wcirwil 
lir      T,  "™^'  "'"  "  ■'  ■""  »"'"l"™  enough  to  be 
flowmg  m  the  same  duectlou,  are  ,,h.e«|  one  »bovc  aud  tU« 


)V 


'1  ' 


(  •■ 


*!ti 


220 


ELECTRICITY   AND   MAGNETISM. 


ill 

I 
I 

II 


ih 


Other  below  a  magnetic  needle,  they  tend  to  produce  opposite  de- 
flections, und  to  neutralize  one  another's  efFect,  so  that  no  deflec 
t.on  occurs  Evidently,  if  they  flow  in  opposite  directions,  they 
tend  to  produce  a  deflection  in  the  same  direction,  and  the  result 
IS  a  deflection  twice  as  great  as  that  produced  by  u  single  cur- 
rent. Ihe  same  result  is  accomplished  if  the  same  current  is 
nuule  to  pass  both  above  and  below  a  needle,  as  in  A,  Figure 
140.     If  the  wire  were  carried  four  times  uround  the  needle,  as 

Fljj.  140. 


I'l  B,  the  mfluence  of  tiie  current  on  the  needle  would  l)e  about 
four  tunes  that  of  a  single  turn.  Very  sensitive  galvanometers 
constructed  on  this  priudple,  often  with  thousands  of  turns 
of  wire,  are  sometimes  called  loi>>j.coil  galvanometers,  in  dis- 
tmction  from  those  having  few  turns,  which  are  called  short-coil 
galvanometers. 

§  175.    Tangent  galvanometer.  —  Th..   arrangement  de- 
scribed above  is  more  commonly  used  as  a  gaivanoscope  than  a 
galvanometer,  though  it  may  be  so  calil>rated  as  to  answer  the 
atter  purpose.     The  law  connecting  the  current  strength  with 
the  (lertection  of  the  nee.Ue  of  this  galvanometer  is  not  known  • 
but  m  another  form,  called  the  tamjent  galvanometer,  the  rela' 
tion  18  expressed  in  a  simple  tangent  of  the  angle  of  deflection 
This  apparatus  is  constructed  on  the  principle  that  the  strength 
of  currents  are  proportional  to   the  tangents  of  the  angles  of 
deflection,  when  the  needle  is  verv  short  in  eompurison  with  tiie 
diameter  of  ^  circle  described  by  a  current  circulating  arouna 


opposite  dc- 
lat  no  deflec- 
ections,  they 
lul  the  result 
single  cur- 
ie current  is 
a  A,  Figure 
c  needle,  us 


^D). 


1(1  1)0  about 
anonietcrs, 
■<  of  turns 
>'■%  in  dis- 
d  short-coil 


c'inent   dc- 
>pe  than  n 
mswer  the 
Migth  with 
>t  known  ; 
,  the  rela- 
3eflection. 
e  strength 
angles  of 
\  with  tile 
ig  around 


EXPERIMENTS   IN  MEASITREMEKTS.  221 

A  magnetic  needle,  about  2.5-  long,  is  suspended  fVeely  by  an  un 
twl^sted  thread  „,  Figure  Ul,  In  the  center  of  a  copper  hoop  „    ",out 
.50-  in  dm,neter,  which  tor.ninates  1„  the  wires  ,nr, ;  and   l"e  e  a^e  Z 
nee  ed  wiU.  the  battery  whose  current  is  to  be  measured      I  ccul^ 
ca  d-board  r..  containing  a  circle  divided  to  degrees  to  Indicate  t^ 
exten    of  deflection,  is  placed  beneath  the  needle.     The  rW  ^^^^ 

the  scale.     When  a  current  passes  through  the  ring  a,  the  needle  i, 
Uetlected.     The  tangents  of  the  angles  of  deliection'm^  be  found  by 


Fig.  141. 


reference   o  a  Table  of  Natural  Tangents  in  Section  Dof  the  Appendix 
and  the  relative  s.rengths  of  currents  nmy  be  determined  hy  the  tiw 
g.ven  above.     A  tangent-galvanon.eter  is  indispensable  to  Z    (  ..lent 
of  electricity  and  one  may  be  made  by  any  one  haviiig  only  ordinary 
mechanical  ability.  "        -  >"uumry 

§  176.  Experiments  in  measurements.  _  Inasmuch  aa 
the  magnitude  of  the  effects  that  can  be  produced  by  an  elec- 
tric current,  or  the  amount  of  work  that  can  be  done  bv  it 
depends  upon  the  strength  of  the  current,  it  is  of  the  utmost 
importance  to  understand  the  principles  by  wlnVh  it  is  remi- 
xuLcu.  ^  raw  experiments  will  make  this  apparent.  Provide 
four  coila  or  spools  of  insulated  wire.  Mark  the  coils  A  li  C 
and  D.     Let  A  contain  100  ft.  (about  1  lb.)  of  No.  16  copper 


I 


II:! 
m 


222 


ip 


ELECTRICITY  AND  MAGNETISM. 


Wire  ;  B  and  C  respectively  80  ft.  and  40  ft.  of  xNo    24  conner 
w.re  ;  and  I)  40  ft.  of  No.  24  German  silver  wire  '' 

V  "rs.  ';o.^^;  TTT-;  ^;X:  t'^;r ''-  - 

Plar.  142. 


Experiment  2.    Place  coil  C  in  tlio  circnit  xsnth  n  «„  i 

each  case  in  tlie  above  exneriiru>nf«    t>.L  ,  «lenectioii  in 

§177.     On   what   strength  of    current   denenrts        u 
appea«  t  ,at  the  strength  of  the  o,„.e„t  varies  „„'t„Tvw-t,7t,e 

o>'cieot   that  „|   co,Kh,ct«™   do   not  allow  the  c„„e„t'to  It 
wth  equal  fac,l,ty ,  f„  other  words,  so^e  conductors  omZl 


FORMULA  OF  RESISTANCE. 


24  copper 


,  in  the  same 

tlio  miniber 

5  for  A,  and 


:impare  the 
it.  Talic  li 

mparo  the 

vc  or  Bim- 
lie  circuit, 
flection  in 
Jrtional  to 
elusion  do 
'lie  third? 


is. —  It 
with  the 

kind  of 
■'     It  is 

to  pass 
er  more 


223 

resfsiance  to  the  passage  of  a  current  than  others.     The  larger 
conductor  offers  loss  resistance  than  the  smaller.     It  is  3 
by  expenment  that  (1)  the  str.n.jik  of  currents  varies  airerJUjas 
the  areas  of  the  cross-sections  of  tU  conductors^  or  the  squares  of 
the  diameters  of  cylindrical  conductors,  inasmuch  as  areas  Jy 
as  the  squares  of  their  diame     -s.     (2)  It  varies  inversely  as  til 
Ingth  of  the  conductor,  i.e.,  if      vire  one  mile  long  offers  a  cer- 
tam  arnount  of  resistance,  a  wire  two  miles  long  will  offer  twice 
as  much  resistance.     (3)   U  varies  inversely  as  the  specific  resist- 
ances  of  the  substances  used  for  conductors.      The  measure  of  the 
conduc tmg  power  of  a  substance  is  the  reciprocal  of  the  meas- 
ure  of  Its  resistance. 

Resistance  is  expressed  in  units  called  ohms^  (see  §181) 
The  student  can  easily  provide  himself  with  a  standard  having 
approximately  a  resistance  of  one  ohm,  by  obtaining  40  feet  of 
No  24  ordinary  copper  wire  0.5--  in  diameter.  The  student 
wi  now  be  able  to  see  that  the  strength  of  the  current  t  a 
cncui  IS  less  when  a  galvanometer  is  in  it  than  when  it  is  not 
in,  unless  the  resistance   of  the  galvanometer  is   very   small 

Tr\  "'1^  T  ''  '"'  "^*  ^'  *^^  ^'--^-  The  resistance' 
of  the  tangent-galvanometer  of  §  175  is  almost  nothing,  while 
that  of  tlie  voltameter  of  §  173  is  very  considerable. 

§  178.    Formula  for  Resistance.  -  Having  found  that  re 
s^tance  vanes  directly  as  the  length  and  inversel^  as  theZale 
ofj^^aneter  of  a  conductor,  we  may  include  all  its  laws  TI 

m  which  R==the  measure   of  the  resistance,  ^  =  the  measure 

0  the  length,  and  d  the  measure  of  the  diameter  "f. 
C3lndnca  conductor.  K  is  a  constant,  such  that  when  the 
inaterialof  thewireis  Vnown  and  the  denominntion  t  wh  ch 

1  and  d  are  expressed,  a  value  of  K  taken  from  a  table  ma^  be 


i) 


■a 


Tfli 


224 


ELECTRICITY  AND   MAGNETISM. 

US  to  find  the  value 


substituted  in  the  equation,  and  thus  enable 
ot  K  ui  ohms 


thous«udto,R  =  0.72xB!;»=„.i,;a„,™. 

When  I  .  e.p„.e<,  io  f„..  „„,  ,  „  ZZ:L  I:^!  ZT'" 

REFERENCE  TABLE  OF  RELATIVE  RESIST 


S"^er.- ^Qoc, 

Copper „ 

Zinc ,, 

Platinum ,, 

Iron '   "  ,, 

German  silver n 

Mercury ,, 


Nitric  acid  — commercial. 


ANCES, 

ETC. 

R«l.  Resist. 
•      I.OO 

K. 

o.ir, 

.      1.06 

9.72 

3.74 

34.2 

«.02 

55.1 

(lie, 

59.1 

13.ai 

127.3 

G3.24 

578.(J 

Rel 

•  Resist. 

•  ('i\  16  to  ''8  O 

Sulphuric  acid,  1  to  12 ,, arts  water    ""      1.100,000 

Common  salt  —  saturated  sol  •  ■    2,000,000 

Sulphate  copper  <<  ',,    3,200,000 

Distilled  water  1«,000,000 

Glass 6'''H)i)0  p """^  ^'''■^''  *'""'  "^'"«f''000,000 

Gutta  percha  ...      rinar, 1'',<JOO,000,000,000 

^     0    C.  . . .  6,000,000,000,000,000,000,000 

risI'"bifti:ro7ii  'T^  'r?""^  ^^^^^^^  ^^  ^'^^  ^-"i--tu..o 

seeond  1st    1  ^'^l^'^^^ '"'<!  the  other  poor  eond„ctor.s  in  the 

second  list  decreases  very  raoidiv  wif).  .,  ..;.    ■     * 

Tlie  resistinpo  ^f   .  r  -  ^  "  ^'^^  '"  temperature. 

th.n  r.f  '''"'''^'  ""^'"'"  "^^t^^«  i«  <^t-teu  much  higher 

than  that  given  in  the  table.  ^ 

§  179.   Formula  for  internal  resistance.  -  Re^istanoo  in 
a  vultaic  circuit  may  be  divided,  for  convenience,  intx>  two  Z 
VI..,  internal  re.stance  (.),  which  the  curreu    encolte^  n 


nrl  the  value 
f  1000  ft.  of 
the  value  of 
ill  feet,  and 
1  equals  100 

distances  of 
*'e  equation 
n  inch. 

ETO. 

t-  K. 

!).!-> 

!}.72 

34.2 

•  •  • .  55. 1 

•  • . .  59. 1 
....  127.3 
....  578.(J 

Kel.  Resist. 

•  .1,100,000 
.•2,000,000 
•..'i, 200,000 
.  18,000,000 
)00,000,000 
)UO,000,000 
)00,000,000 

iiI)oratur<! 
•'.s  in  the 
l^erature. 
-h  higher 


^t.anno  in 
o  parts ; 
uters  in 


ELECTRO-MOTIVE   FORCE. 


225 

passing  through  the  liquid  between  the  two  plates  in  the  cell 
and  exlernal  resistance  (R),  which  it  suffers  in  the  renuainder  of 
Its  path.     The  internal  resistance  is  governed  by  the  same  laws 
as  the  exteinal  resistance.     In  this  case 

ineasiire^otjlistJince_ofJhe j^     apart  (/) 


r=K 


measure  of  areas  of  the  plates  submerged  (rF; ' 


QUESTIONS   AND  PROBLEMS. 

1.  What  length  of  copper  wire  avIII  have  the  name  resistance  as  a 
mile  of  iron  wire  of  tlie  same  diameter? 

2.  How  can  yon  reduce  the  resistance  of  an  iron  wire  to  that  of  a 
copper  wire  of  t);.i  .same  lengtli? 

3.  Abo-^  h  ,  -,  much  is  tlie  conductivity  of  water  affected  l)y  addinij 
a  little  snlji  ;;  .   acid?  " 

4.  How  many  times  greater  is  the  resistance  of  dilute  sulphuric 
acid  than  tliat  of  copper? 

6.      Upon  what  does  the  resistance  otfered  uy  the  liquid  part  of  a 
circuit  depend,  and  how  may  it  lie  diminished? 

6.  What  is  the  resistance  of  500  feet  of  copper  wire  .014  inch  in 
diameter  (No.  30  B.W.  gauge)?    Ans.  24.7  +  ohms. 

7.  What  lengtli  of  copper  wire  .00«  inch  in  diameter  (No.  38)  will 
offer  a  resistance  of  1  olim? 

8.  What  is  tlie  resistance  of  16  yards  of  German  silver  wire  CNo 
30)  .014  incli  in  diameter?  ^      " 

9.  What  Is  the  resistance  of  1  mile  of  iron  telegraph  wire   the 
usual  size  being  .175  iiicli  in  diameter? 

10.  Express  in  ohms  the  resistance  of  1  mile  of  copper  wire,  O.OG 
inch  in  diameter?    Ans.  0.72  X  ^'^  =  14.25r,  ohms. 

11.  In  Experiment  2,  §  17(!,  why  is  tlie  current  when  C  is  in  the  cir- 
cuit alone  not  twice  the  current  when  15  is  in  the  circuit  alone?  From 
the  results  of  tins  expiTiment.  an<l  tlie  laws  stated  in  §177  estimate 
the  internal  resistance  of  tlie  cell  u.sed.  In  .solving  (1^;  prohlem  vou 
may  assume  that  tl.e  electr. .-motive  force (§  180)  of  the  cell  remains'the 
same,  tliougli  the  resistance  of  the  circuit  is  changed.  The  above  as 
sumption  is  not  strictly  ti-uc  (§  isi). 

§180.  Electro-motive  force. -The  experiments  de- 
scribed n.  §  151  show  that  electri.-ity  constautiv  flows  in  a 
closed  circuit  containing  a  voltaic  cell;  hence  the^ cell  has  the 


3 


iisr 


!!'!! 


ill 
If 


ELECTRICITY  AND  MAGNETISM, 
power  of  Sottino-  eleefrioifv  ,„  .     ^- 

(..sualivabbrevk    d  E  m'fT      uT  T  ""  *«"-°-''-'™  force 
depends  solely  „„„  ^f.-^:*-     "has been  f„„„d  that  E.M.P. 

about  the  K.M.F.  „,  o„e  grtit  J,'  ^Th  1  V  "°"-'    "  '' 
exh,b,t.  the  .,e„t.o-,„„tlve  force  h^vo^S^fdi;™?.!:'''^ 

Buasen  and  Gmve ^'^^  *°  ^-^^  volts. 

Leclunche,  at  first l"i>  to  l/Jo      " 

Grenet  <«       ' 1-48  to  l.fio      " 

Smee 1-80  to  2.3 

• p^ 

oU^^^Z:\Z!::^  "S^^r  ^^^^^^ ^^^'^"'^"the'circuit  is 
Will  require  195  Since  cells  t  ,'h  c  ho  "^""^^''  '"'"  ^"'**^»^^'  ^^at  it 
ln«h  resistance)  as  would  be  fe^ive  .  h  fi5  gTo':  '"T"'  *"  '*^  ^'^^"**  (^^ 
sary,  i„  order  ^,hat  this  statement  mav  ho  ^^  ''"'■  ^^^^  '^  ^'  »«^'^«- 
.^^.ma-f  r«t.^anc.  should  be  high?      ^       approximately  true,  that  the 

§  181.    Ohm's  Law Tbr.    i 

strength  of  the  current  and  is  (hn  ,' • '1''  '-^P'""''^«  ^^'^^ 
calculations  on  curr  nt  '  ^    ei  T"'  ^^  "^"^'  n^athematical 

0^>n,s  La..  Call  ;  ^^Zfc  tl"  K  M  ^"""^  '^"^^"  ^ 
the  whole  -istanco^a  hT  "  ,t  R  t,w  T'''  '^' ^"'^ 
the  law  is  ^  ^  '  *'^^  ^o™"la  expressing 

H' 

In  words,  this  means  that  the  strenuth  of  fh.  . 

the  electro-motive  force  nf  //>«  a   "^"^  ..''•^  '^'^  c«'-'-e««  w  e(?/«i/  /o 

the  ciraut;  i.e.    C  ^^{elr'^^  f  ""^'^  '^  '''  '•^«'^^'-  «/ 

but  will  b;  less  wLr  nr''  r  ^ ""  ^  ^'■^^*^'-  -^-' 

^"  "  '^  &•  "^^t-"'-.  ^"J  greater  when  R'  is  less. 
"~        ''°^  E  "'''^"  ^"^  ^-'--ternal  resistance  is  considered 

1  Voit,/rom  the  name  Volta. 


Oim'H    LAW. 


notive  force 
lat  E.M.F. 
'  substances 
dependent  of 
5  unit  em- 
iolL'  It  is 
wing  table 
cells :  — 


raits. 


227 


le  circuit  is 
»ce,  tliat  it 
circuit  (of 
is  it  neccs- 
ie,  tliat  tlie 


3Pes  the 
lematical 
:nown  as 
y  E,  and 
^pressing 


equal  to 

tance  of 

or  less, 

13  Jess. 

isideied 


S-me'rf™  T^  ";*^"'"^'' --^' »'«  --erted  thus:  calling 
the  foimer  R,  and  the  latter  r,  tl.o  uxpresBion  becomes 


C 


R-fr 


.-rrent  has  a  va.ul     '  T^^l  "■;';^   •-  »reg„„,ec.    t„e„  the 
I.-  a  resistance,  B,  eq„a,  to',  „:,„,"tl'l;'  ""  """""'""^  -^ 

between  the  two  ends  of  r   ll      "  '«  «^"^'tb'  the  same  as  that 

-  pc^ts  at  ^t:rz:\;::ti::r^ 

.o„r,a„ge„t.,aL„o™ter7o  Ci^tT     '  """^"""^ 

as  we  expressTnTmou:t  ofTo  "1  rdT""T'-7^"* 
or  a  „,ass  of  coal  in  the  dZmC  on  ^""7"^'""  ''"'^^''^^ 
electrical  a^uomlnut.on  pounds,   we   express 


ii^;f^ 


M 


! 


000 

ELEGTRlorTY  AND  MAGNETISM. 

Potential,  P  (commonly  difference  of  P) . . . .  i„  volts 
Electro-motive  force,  E  , 

RosistanccR '''''*•''• 

Stren-tli  of  current  C "  **^'""'* 

Quantity  of  electricity .!  '''''^^'''^• 

rp.      -,  „      .  coulombs. 

Ihe  foIlovviDg  will  give  some  idea  of  the  maffnitndp  .f  ,u 
|lenon.,nations.  A  g.-avity  cell  produees  a  diSce  of  ,^ot  n' 
.a  o,.  an  eleet.o-motive  force  (lor  these  are  onl  diff  ;e  rwl;" 
of  viewing  the  same  quantity)  of  nearlv  1  volt  ^"'"^"*  ^^^^ 
«P-k  1-  long  requires  f romVoOO  l\  o  'olts  T^Zl 
ordmary  copper  wire,  250  feet  long  (diameter  05  in/ 
2  lbs.),  hns  a  resistance  of  about  Llir  A  t  1o  fTef of 
copper  w.re,l™™  in  diameter,  has  a  resistance  of  l  oC     a' 

rent  whose  strength  is  h  aJpLt  ''  '''''''  "'"  ^  ^-" 

^^w.lupon.eeentimUgran::;td::^^^^ 

called  C.G.S.,  or  absolute  units,  has  been  devised  A  r- 
s.on  of  these  units  is  altogether  beyond  the  ir^tr  'f  ttis  bo^ir 
but  any  student  wishing  further  instruction  concer  in.^K  : 
system  may  read  Maxwell's  Electnoitn  nnrl  nr  "^''"""^  ^^'''s 
collected  reports  of  the  Com^t  ft  ISTsr'  T  "^^ 
Electrical  Standards.  Association  on 

The  absolute  units  have  approximately  the  following  values : 

Absolute  unit  of  E.M.F.        =J,vnif 

'*       I^esistance  =  Jp  ohm. 
"        Current       =  10  ampcVes. 

Tf„-ii,       ,  ,  Quantity     =  10  coulombs. 

It  will  be  observed  that  the  formula 

holds  true  also  when  these  units  are  used. 


ARRANGEMENT  OF  UATTEKIES. 


229 


3S. 

lbs. 

ide  of  the 

of  poten- 
rent  ways 
produce  a 
A  No.  16 
h,  weight 
>0  feet  of 
hm.     An 
f  i  ohm  ; 
ire  a  cur- 
id,  which 
electrical 
»d,    and 
^  discus- 
lis  book, 
ing  this 

and  the 
ation  on 

values : 


I 


Fig.  143. 


PROBLEMS. 

1.   What  current  will  ho  obtained  from  a  gravity  cell  when  E  =.  1, 
r  =  2  olmis,  and  R r.  lo  ohms? 

^istancc  js  3  ohms,  and  external  resistance  is  8  ohms? 

3.    What  cnrrent  will  a  Grove  cell  furnish,  having  the  same  Internal 
and  external  resistances  a,»  tho  last?  internal 

§  183.   Arrangement  of  batteries.  _  The  internal  resist- 
ance may  be  diminished  by  placing  the  plates  as  near  to  each 
other  as  practicable,  and  by  employing  large  plates,  and  thereby 
increasing  the  size  of  tho  liquid  conductor.     But  it  is  not  always 
convenient  to  employ  very  large  plates,  or  we  may  have  occasion 
to  employ  a  battery  for  certain  purposes,  as  we  shall  see  pres- 
ently, m  which  Inrge  cells  would  be  of  little  or  no  advantage. 
The  same  result  that  can  be  produced  by  a  single  pair  of  large 
plates,  may  be  obtained  by  connecting  the  similar 
plates  of  several  pairs  in  separate  cells,  thereby 
practically   reducing    several   pairs    to   one   pair 
having  an  area  equal  to  the  sum  of  the  areas  of 
the  several  pairs.    Figure  143  illustrates  a  method 
of  connecting  cells  for  the  purpose   of  reducing 
the  internal  resistance.     This  is  called  arranging 
cells  parallel,  in  multiple  ore,  or  abreast. 

This  arrangement  is  very  effectual  in  increasing 
the  current-strength  when  the  internal  resistance 
is  the  principal  one  to  be  overcome.  For  instance, 
call  the  electro-motive  force  (E)  of  a  single  cell 
1  volt,  its  internal  resistance  5  ohms,  and  let  the 
plates  be  connected  by  a  short,  thick  wire,  whose 
resistance  may  be  regarded  as  nothing;  then 
^  =  7  =  5  =  -2  ampere.  Now  connect  10  similar 

cells  abreast.     The  size  of  the  liquid  conductor ■ 

being  increased  tenfold,  the   internal  resistance   is   one-tentb 
as  large,  and  we  have  0  =  5=1  ^-^=2  amp6re..  So  that, 


'  iiii 


m 


230 


ET.ECTRICITV  AND  MAGNETISM. 


^hen   there   is  no  external  resistance,  the  curr^f  ' 
the  size  of  the  plates  ,s  increased      tL  1  '^"'''''  ""' 

fuo  in  ease  the  external  r^JZ^',  '^ZryZl  ;;PP-xin.ately 
with  tlie  internal  resistance  ^  "  co.npariscn 

.  y^'^  '-'  ''-'^'-'  ^^"-'  -  '^bove,  hut  the  external  re- 
^'""^"^="^^^'-'^^-^-^-.0048.a.p,re.rf 
10  pairs  are  connected   abreast,  C  =  __l 


Fig.  144- 


4.  .f^  ~  "^049+  ampere. 

lessening  r  has  little  effect ; 
80  there  remains  only  one 
way,  viz.,  to  increase  E,  the 
electro-motive  force.  How 
may  tliis  be  done?  If  the 
current  from  a  cell,  instead 
of  passing  immediately  out  of 
the  cell  on  its  journey,  is  made 

the  KM,K.  ^:.:2:::::^zi2:z::i^r 

one,  and  that  fhp  r  \r  jp   •  .,  ^'itLer  resuic  is  the  true 

U.0  clootro-motive  force  a  esridt  b    in     ^    ''  ""  *"  '""'''''<' 

T.>e  method  of  conuect tag  .^1^^  Z  '"  """•"  "•"*»• 
l''igure  144.  ^  ""^  '™  Purpose  is  shown  in 

It  will  be  seen  that  in  the  multiple  are  (Fi»  I4S^  »II  ,k„    • 

een  is  connected  wit^'tiiixrortrs.T i::;c.  °'  °- 


ARRANGEMENT   OF   RATTERIES. 


Fig.  145. 


231 

In  the  last  example  given  above,  let  us  see  what  wonkl  be  the 
effect  of  conneeting  the  10  cells  in  .eries.  In  this  case  E  is 
increased  tenfold  ;  and,  as  the  current  is 
obliged  to  pass  t])rough  tlie  liquid  of  10 
colls  inst(!ad  of  one,  the  internal  resistance 
will  also  be  increased  tenfold;  hence 
r  _         1  X  10  _,^ 

(T-^^^^y-^;^  =  .0400anip6re,  more 

than  eight  times  as  much  as  before.  Tims 
it  appears  that,  ivhen  the  external  resistance 
is  large  in  comparison  icith  the  internal 
resistance,  the  current  may  be  largely  in- 
creased by  multiplying  the  cells  in  series; 
m  other  words,  by  forming  a  lattery  of 
great  electro-motive  force.  In  long  tele- 
graph lines  the  battery  is  made  up  o'f  hun- 
Pig.  140.  d  r (! (1  s     of 

cells   joined 
ill  series. 

Large  cells  are  used  simply  be 
cause  the  fluids  last  longer,  and 
so  tlie  cells  need  less  attention. 

Sometimes  a  coml)ination  of  the 
two  ai-rangements  gives  a  stronger 
current  than  either  alone.      The 
cells  may  be  grouped  together  in 
pairs  (as  in   Figure   14')),  or  in 
triplets  (as  in  Figure  14G),  so  as 
to    increase    the     electro-motixe 
force;    then    the   several   groups 
may  be  connected  abreast,  to  reduce  the  internal  resistance. 
Uie  strongest  current  is  obtained  by  such  an  arrangemont  of 
the  cells  as  makes  the  internal  resistance  as  nearly  as  possible 
equal  to  the  external  resistance. 


^11 


232 


ELECTRICITY   AND   MAGNETISM. 


I!     : 


PROBLEMS, 
hattor,?  ""  ■"  "'""•  "'""  '""■'■••'  "ill  i.»  iiol  from  the 

HiJ^inSr;:;;:::;:::::  ::„:  ^;'^«.7'.-"'- , o,  ..„«,  ,vhc.„ 

cm-nt  of ''«!;:;■:";:;;:: '■"■"!''''"'  '■■'  -  ""-■  >»  (ou„u  t„  rc„„,rc ,. 

If  the  cirailt  coSsof  r,        """' """'y»'™"y  «■-■"»  "i]Utm,ul,,, 
smvity  «.11»,  oaoh  of  3  oh,„,  reik  w    ^  '"  °''  ""'"'^^"'>  "'  »" 

w,,>;,/aXr'rrs';r-',o",:r^ ";  ""■"  '=■«" • 

«■    By  mca„,  „f  v„„r  tan"™,  „7i  "''""  "  =  •'«'  "l""»? 

obtalnc,  „,.  ,Wcrc.„tU,,gS     Jf;!""?""''  """""«  "'«  ■^""-"» 

e..™a>  .,..„. .  ,0,.  (.,  :r.;:'v«:  „r,  ,Z;iL>  *"  •" 

halTe-folfot-riaSr ""-'^  '"'^^""'  ""^'-^  -"M 
1.     /( toouUUave  a  khjh  electro-notive  force. 

the  „se  to  which  i^^^;^t::zi:rr"''"^''' 

about  7,000  oh„.,\v  a  outlt  ,'  '       '""    "''^""'™    '' 


geiiemtoU  in  n  ladv's  tl 


limbic. 


GENEllAL  <;ONC'LU8IONS. 


•  increased 
'■  from  the 

oil;,',  wlion 

each  fell 

e,  and  the 

require  a 
it  require, 
.  iliameter 
i? 

11)  of  210 
esistance 

=  .8  ohm. 
oJims? 
currents 
t'hen  the 
igh. 

would 


ince  of 

ce. 

actiee, 
id  the 
which 
is  the 

wire, 
leedle 
same 
been 
L!e  is 
nble. 


238 

and  the  signals  produced  were  as  dislim.f  ,.     u 

qua„„ty  „f  „|eetn„ii.v  that  |„«,,.,    ,,,_    , ,.    '°,     "»  '=««''  «!■« 
h-M.I-.  ..f  ll,c  l„ttc.,.y,  a„;„„t  U|J,U,-. ''''';"  "" 

-o  con  w„„l„  f„s.  the  i„eh  owi     it ,;,"':  ""."•    ,«'"  »'"l" 
the  ujile  of  wire.  strength  of  current  in 

A  battery  of  three  cells  arranged  abreast  will  f.. 
length  of  platinuni  wire,  but  will  not       rf,  "  "^  '"''*^'" 

the  poles  in  his  l^^nds  ;  ;hi.e:    I^.^  ,?'      ;>;.:,|--"  '!'^'<'-^ 
not  fuse  the  same  wire   b„f  win         7  "^  '"  ^^^'''^^^  "'H 

<l"cti„g  |,„„.er  of  a  ,,ar8o„'»  b,„ly"  ••■""^""■.g  the  cou- 

..po„  t„o  „ea,.„„.  o^f ;:  r,:: :  r  r^^^^^^ "» --  -" 

»"d  to  k«.|,  the  curct  near  the  core  IZ    '         '•'""l'»°ta««s, 

Butaio,,,.  thin  wire  wo,,,.,  o;,^",:;  ."riZr:'.^^  "";'• 

so  reduce  tl,e  e„rre„t  a»  to  ,„ore  tl,..,,  , ,«■!„? '      '*  '"'»''" 
wou,.i  ot,,e,wi.se  be  ,r,in,.,l    T.  [        ''"  '"'™n«"ge  that 

'"  -  '^n-cuit  with  otiL  large  ;Lto,,e,,",""^'  ''  '"  ""  ™"' 
^  l.e,ix  of  ,„a„.v  t„r„.  of  Z^^^Z'J^"^  '""■«"-'»"  »' 
co,n,.a,-ativelv  ;  so  the  at,e„.„l,     ,  '"'"'"  '■'distance 

core.   Fo;t,,e.a™eCo,f  :;:;       ''  '7'-"  "'-»™t  o„  the 

in  c.e..it„  Where  n,.:::^::^-^^:;^^;:^: '"  r 

few  turns  of  large  wire  •  but   if  ;*  ,•    ♦    i  '  ""  ^^nttim  only  a 

an.,  it  .,o„u,  ^ontai,';  ^^^ .'  ii:::^:^^  ""■^^^'''- 


!  'r 


fil 


234 


ELECTRICITY  AND  MAGNETISM. 


QUESTIONS. 

mL![  '!iV°7'^«»>'"St'^°  •«  to  be  rung  by  tho  action  of  an  olcctro- 
magnc  I.    The  current  used  comes  from  a  battery  u.  Now  Vn/ir      ,r 
should  the  olectro-magnet  be  constructed?  ^  ^'"'^-     "°^^ 

2.   If  you  wished  to  njeasure  the  current  bv  the  \utrnrU,r.n 

S-   Would  It  require  a  different  fc-alvanometer  If  It  were  to  I,,  h  r , 


./.' 


if* 


r... 


XXXI.     MAGNETS   AND   MAGNETISM. 
^  ^  ,^-  .^^^^anent  and  temporary  magnets.  -  One  of  the 

know  how  It  can  p.ck  up  bits  of  iron  and  steel.  By  the  aid  of 
a  small  instrument  already  st^died,  we  may  uiake  a  plir  of  mul 
magnets,  and  study  their  actions  and  laws. 

Experiment — Take  the  electro-magnet  describod  in  r  17, 
couple  of  sewing-needles  or  larger  steVrods      Vm  1     .>,^  ^"'^  ^ 

o?  mn    h^t  '•  ^u-o-magnet,  possess  the  power  of  attra^tin^bi 

"c:  i:st  rirrd::sr '  "^  ^^^^^  ^^  '-^  *-  --  -« --" 

Both  of  them  exerted  that  peculiar  force  called  magnetic  force, 
or  possessed  the  property  called  magnetism;  that  is'  both  w7r 
magnets ;  but,  as  the  steel  retains  its  power,  it  is  called  .perZ 
nent  magnet  to  distinguish  it  from  a  temporary  magnet,  hke The 
non  w.re  or  the  electro-magnet  itself.  The  o^ialit?.  of  steel  bv 
which  It  at  first  resists  the  power  of  magnets,  and  resists  the 
escape  of  magnetism  which  it  has  once  acquired,  is  cal    d  coe 


Law  of  Magnets.  03 '' 

"a.*,.c„  i,.„„  po.Le,  JioZ^xr^:::^  r""- 

01  eloctro.„,aguet.  should  be  ma.le  „f  the    "LI'  lV,7 
...ay  acquire  and  part  wit,,  .a,.  .,..„  U.Jl^Z;.     "'  ""•■' 

and   severs:  te^t    """"'"'"  '■<•"-•".  ''3'  «"ca<la  that  will  „„t  „„twlst, 
distant  from  each  i-  ig.  147. 


other  (v.  Fig.  177, 
§211).  When  they 
<'ome  to  rest  no 


Pcrraanoiit  Magnet. 


IC^ 


Inducfd  Nfagnets. 


..ear  to  the  markoTcnd  of  theU",,        '%""" '""'''"»' """'  "'  ""» 
one  «.„.„».     C„rerXt*°,,:rn,.freL''':je"'"°*"'  °"*  "'''' 

We  discover  tlie  following  law  of  magnets  •    ;-*.  .,„; 
whTe  poles  attract  one  amtlr.  ""'""'"•    ^^^  Poles  repel, 

two  mas„et».     I)oc"  ^e  Uele  ,» '.ffT'''  "5  """X"-''.''".!-' .>« ween  ,l,e 
«ny  effect?    InterpLaTI^r,     ,  """'  ".I"'™™'  Produce 

What  1,  the  St°  '■°'"""°"  """■»''"  ".=  '"••>  """S»«. 

Substances  that  are  not  susceptible  to  magnetism  are  like 
glass,  paper,  and  wood,  mag„eticalhj  tran^arent.  When  a 
magnet  cause,  another  body,  i„  contact  with  it  or  in  itTn  W> 

tbat  tody,  ».e.,  .t  .,yi„e«ce»  U  to  ie  like  itself.    As  ftt^acUr 


!l 


III 


If 

''I' 

i>' 

li 


236 


ELECTIIICITY  AN1>  MAONETrSM. 


netized  ,  ,ece  of  non  or  steel,  it  must  be  that  the  ,„a..„etism 
ndaee..  n,  the    „t,e..  i,  sueh  that  o,.„osite  polea  are  adle 
that  .s,  a  N  or  +,.„,e  induces  a  S  or  -pole  ..ext  itself,  as'show,; 


in  Fig 


147. 


§188.    Polarity.- Experiment  I.    Strew  iron  filings  o„  a  flat 
*"  surface,  and  lay  a  bar-nKii^nct  on 

tlioni.  On  raising  tju.  maifnot,  liow 
!in>  tlio  fllin;;fs  wliicli  cling  to  it  dis- 
tributed?   What  does  thl,s  prove? 

Magnetic  attraction  fs  greatest  at  the  poles,  and  diminishes 
ton:a.ds  thec.nter^.here  it  is  nothing,  or  the  center  of  tke  bar  is 
neutral  Tl.e  dual  character  of  the  magnet,  as  exhibited  in  its 
opposite  extrenufes,  is  called  ;>o^anVy,  and  magnetism  is  stvled 

VT?7^r  '  !^7^-^-^-'--^titsn:,tndli„e,as-I 
i^xp.  1,  §  25,  It  IS  found  that  equd  and  opposite  polarities 
Fig.  149.  exist  uiiere  there  is  ordinarily  ,h) 

=     evidence  of  them. 

Fxperimeiit  2.     I'lacc!  a  copjior  wire, 
„P    ,        .  .  tliroiigli    whicli  a  vcrv  stroiiir  cnrrcnl' 

w,rr«;:';::,:;:r""' ' """'' --^----....r: 


H 


This  exper.ment,  and  those  with  the  electro-magnet,  and  the 
deflecfon  of  the  magnetic  needle  hy  an   electric  J^.rrent,  and  a 
"Altitude  o    others  that  the  pupil  will  meet  with,  cannot  fl 
to  convince  h.m  that  an  intimate  relation  exists  between  elertricit,, 

ert.es,  yet  ahke  .„  many,  and  almost  invariably  accompanvin  . 
one  another,  and  con  <  nUly  .nerging  one  into  the  othe^u  p^ 
as  If  they  were  only  different  manifestations  of  one  and  he 
same  agent.  "^ 


ATTRACTION   OF  CURRENTS. 


237 


§189.   Attraction  and  repulsion  between  currents.  ,- 

Let  us  study  still  further 
the  properties  of  the  cur- 
rent. 


Battsry 


Experiment  1.  Suspend 
two  copper  wires  (Fig. 
150),  eacli  50""  long,  aud 
about  5"""  apart,  with  their 
lower  extremities  dippiug 
about  2'"m  into  mercury,  so 
as  to  move  with  little  re- 
sistance either  toward  or 
from  each  other.  In  Fig- 
ure 150  the  current  divides 
itself  and  flows  down  both 
wires  to  the  liquid,  so  that 
that  part  of  the  circuit  presents  parallel  currents  flowing  in  tlie  same 
dn-ection.  Figure  151  is  the  same  apparat.is,  with  the  connections  so 
made  that  the  current  flows  down  one  wire  and  up  the  other,  and  we 
have  an  example  of  parallel  currents  flowing  in  opposite  directions. 
What  IS  the  result  in  the  first  case? 
What  in  the  second  ?  What  conclusions 
do  you  draw? 


FiK.  152. 


Hence,  the  First  Law  of  Cur- 
rents :  Parallel  currents  in  the  same 
direction  attract  one  another;  2)ar- 
allcl  currents  in  ojyjwsite  directions 
rejyel  one  another. 

An  interesting  illustration  of  the 
former  part  of  this  law  can  be  ar- 
ranged as  in  Figure  152.  A  bat- 
tery wire  is  bent  in  the  form  of  v. 
spiral  coil.  At  a  the  wire  is  broken, 
and  one  ond  dips  just  below  the  surfnee  of  morcurv  in  a  <rlaps, 
while  the  other  end  is  i)laced  in  the  same  liquid  at'  a  little  dis- 
tance from  the  first.  When  the  circuit  is  closed  the  current  will 
be  parallel  with  itself,  am]  will  (low  hi  the  same  direction  Ju 


iiii 


238 


ELECTRICITV  AND  MAGNETISM. 


the  n^ercur,  and  break  Ih^  ^T  T  ^^  ""  ^^^^^  ^"*  ^' 
attraction  ceases,  a.Kl  the  coil  is  Zt  \  "''""'^  ^'^^^°'  t^e 
of  gravity,  and  closes  the  circu.r"  ""  ''^^"^  '^  ^^^  ^^^^^ 
vibrator,  .notion  is  l>rodnce<l  inthe  cf" 'rr"'  ''"^  ^'^-^-^ 
bo  -nade  with  considerable  care  or  it  wll,  n';':.::^'"^"* '"^^ 

^.pcH^ent  ..    Prepare  a,,....  ,.  .,,resonte.  ,„  ,.,,re  .. 

a;"l  5™  u,ick,  cut  a  circular  hole 

;;"""t  4- in  diameter,  and  insert 
'   f^'la^s   test-tufje   b,  about  6cm 

'  lon^'.  that  « ill  j„st  fit  in  the  hole. 

iiikcan(No.L^O)  insulated  copper 
>vire  about  200- long,  ,,i„^,tj,^ 

l^entral  portion  into  a  coil  c,  12cm 

ong  and  15.nm  i„  diameter,  with 

turns  about  3mm  ^part,  leaving 

about  12cm  at  both  extremities 

"nwound.     To  these  extremities 

Holder  strips  of  copper  and  amal- 
fc'anuited  zinc  about  3cm  io,j„  g,,,, 

as  wide  as  the  interior  of  the 'test, 
tube  will  admit,  and  allow  them 
to  be  separated  about  5mm.    j^. 
sort  them  in  the  tube, 
and  cover  with  dilute 
sulphuric  acid.  In  the 
center  of  the  coil  lay 
a  No.    16    soft   iron 
wire  ,1,  and  float  the 
>vhole  ill  a  vessel  of 
water.  The  apparatus 
floating  battery  and  electro-magnet     Rr.„„         ^°"ft'f"t^«    a    small 
inagnet,  or  a  short  piece  of  soft  . I"..       ^'  "'"  ""'  "^  '^  Permanent 
stirrup  „,  near  to  one  of  the  jioles  ,  f  hi!   '  "'  "i'T"'^'''  '"  '^  P"^*''' 
a»d  prove  by  experiu.ent  Lat^olonlJ^  "'  the  Hectro-magnot, 
respect  like  a  magnet  ^  '^'^  '''''■"  ''^'^ave  in  every 

E.peH„.e„t  3.    Bo„,„ve  «„  „„„  ,,„  ,„,„  .„^  ^^^^,^^  ^^^^^^_ 


ATTRACTION    OF   CURRENTS. 


239 


"enx,  as  in  Figure  154.     In  this  position   the  two  currents  flow  in 

t'endrtoVf  '"^."^  '^  ""  """"^^''-     l^'-cliately  the  c'l   1.1!"    d 
ends  to  talje  a  position  at  right  angles  to  the  wire  above,  so   hat  the 

i"  Fig;;:r;55. ""''  '"^  ^° '''''-'  ''•■^"^^  -^  ^^  ^^^^  --  ^i-r^  a: 

Hence,  the  Second  Law  of  Currents:  ^«^«?a,- c^rren^.  ^em?  fo 
Z'c^come  pam^^^Z  a»,rf>z«  /„,  the  same  direction. 


Fig.  156. 


Observe  that  the  action  of  the 
helix  in  the  last  experiment  is 
analogous  to  the  deflection  of  a 
magnetic  needle  by  a-^  electric 
current. 


Experiment   4.     Place    opposite 
one  end  of  tlie  floating  helix  a  second 
helix  Figure  156,  in  such  a  manner  that  the  currents  in  the  two  helices 
may  have  the  same  direction.    The  two  poles  of  the  helici  att mc 
one  another  i„  conformity  to  the  Fir«t  Law  of  Currents.     Reverse  the 
po  es  of  the  helix  in  your  hand  so  that  the  currents  will  flow  hi  opp  " 
8,te  directions,  though  still  parallel;  they  repel  one  another.     (Why?) 

The  two  helices  appear  to  be  polarised  like  two  magnets,  and 
tor  many  purposes  may  be  considered  as  magnets.     Observe 
that  at  one  pole  of  each  helix  the  current  revolves  in  the  direc 
t.on  that  the  hands  of  a  watch  move,  and  at  the  opposite  pole 
It  revolves  ni  a  direction  contrary  to  the  movement  o'the  hands 
of  a  watch      Bring  the  north  pole  of  a  bar-m.gnet  near  that 
pole  of  the  hehx  where  the  motion  of  the  current  corresponds  to 
tlie  movement  of  the  hands  of  a  watch.     They  attract  one  an- 
other;  but  if  the  same  pole  of  the  helix  is  approached  by  the 
south  pole  of  the  magnet,  repulsion  follows.     Hence,  that  is  tiio 
south  pole  of  a  iielix  where  the  current  corresponds  to  the  motion 
of  the  handsof  a  watch,(8),  and  that  is  the  north  pole  where  the 
ourront  IS  in  the  reverse  direction,  (n).     B„t  the  important  les- 
son derived  from  these  latter  experiments  is,  that  helices  througk 
which  currents  are  Jlomng  behave  toward  one  another,  or  toward 
a  magnet,  in  many  resjwcts  as  if  they  were  magnets. 


!  M 


'"Hi 


I  i 


m 


240 


KlECTKIcm-   AND   MA.i.NE-nsM. 


§190.  Ampere's  theory,  _Thp  (v,„t.     ■■  , 

a....  thus  eve,.,  moleo^k^e  1  ' ;  Z.^T  "'"""■°"''^-' 

plane.,,  an.,,  „,,■'  ,o  ,  i  v  j  ,  ?™*  ""  '"  ""  '"-""'^ 
another,  and  so  theh-  fee  f,t  "■""""'  ""•''  ""''''''''<'  ""^ 
of  eleetricity  or  a  m  JneT ,  ^       "  '"  '■'"'■     ''"'"■'' ™™"' 

«a.ne  dh^eetion,  ilZZXru    'T'""  '"""=^'  """  "'  ">« 
If  the  coercive  force  isT™  .      '""'  ^"  '"'  <^"™'"»- 

attained  on  the  ™ov  I  of  t    "  'T"? ''  ""'  '""""'^''""^  "»  "e 
".agnct  is  the  relnU  '"""""S  '""'^'='  ""^  »  i'e™ane„. 

Intensity  of  magnetizalion  denentk  on  fl,„  ,, 

-..  and  .he  latt..-  depends  onTi  f  t,™, .,     TtT      r°"^'- 
nnigiiet.     When  i|„,„.  „„.,.„„.    .       ""ength  of  the  ujilnen  M,g 

!»<-.V  l.as  reeeived  al,  th,:   C      „"  j;™;";'  ""'^^r^^'-    ■>" 

"'U,  and  i,  said  to  he  m.^^.tl^^X^Z'         T"'"" 

"^'"^"o"  '''•«  ciu-rents  really 
i^i^.157.  ^"•™'''^toarouncUheinaivid.,aI 

molecules,  jet  the  resultant  of 
these  forces  is  essentially  the 
same  as  if  the  currents  circu- 
lated   around  the  body  as   a 
whole.    Figure  157  represents 
sections  of  a  cylindrical  macr. 
net,  and  the  inchukui  circles 
the  circulation  of  the  seve,al 
currents  around  the  molecules 
b'"'g  in  these  sections.    Itvvii' 

contiguous  sides  of  any  two  of  .-t!!'"."  ?'''^  *''^  "'"''""^^ '^^  ^'''' 
directions.  .nn,l  tho.-JeT,  f  ""'''''  '"^^''  '»  «!>P'^«i^« 

currents  that  pass  a^;::::^  -----=  ^^'^'^^'  ^"« 
so  affected.  •^""utitnte  of  the  magnet  are  not 


AUVkllK'n  TIIKOUY. 


241 


The  hypothetical  c.irrcM.ts  that  <.|r(,„1ato  around  a  ma^netio 
molecule  we  shall  call  A.,^,r^an  currents,  to  dis  L^.rl 
from  the  known  current  that  trav.rHen  the  helix.  In  strict  aocor 
a..ce  with  this  theory,  the  p.U.  of  the  eIectro-n.ag:  e Tt^ 
mmed  by  the  direction  of  the  c.UTent  in  the  helix.  The  inductTvo 
influence  of  the  electric  current  can.,  the  Arnp6rian  cu  .  lo 
take  the  same  direction  with  itself,  uh  represented  in  Figure  158 


Vlu,  J/W, 


kuo«  pi  enomona  of  magnoti.m,  It  ,ho„M  be  home  h,  mi„.l 
that  physicts  of  this  generati,,,,  vah.o  the  theory  rathor"  a 
L  Ip  to  the  ™agi„atioua.,d  ,„e„,„.,,  ti,a„  a,  a  uL  staten^  nt 
of  tl,e  faets  It  ,s  nearer  the  t™th  to  -  -  that  the  moleeules 
are  po  anzed  as  if  eurrents  were  circlat,,,,  around  them  „ 
the  actual  e.„te„ee  of  ,„„h  e„rr«„t»  we  k„„w  nothing.  8„ 
also  of  the  real  nature  of  polarit;,-  wo  know  little  or  nothing. 

EXERCISES  AND  QUESTIONS. 

1.  Regarding  your  lead-pencil  aH  a  rod  of  imn   nnH  „    *  . 
electric  wire,  tie  a  knot  at  the  .,u,  lullZrZf.l         "^  ^^  ''" 

2.  What  would  be  the  effect  of  rcvcrsltiK  ♦ho  current? 


curreat., .  h,  K,,„re ,«».  ,„,.„„„  :::i:c:2^:::^ 


m 


242 


ELECTRICITY  wND   MAGNETISM. 


.J'  .?^  ^'l''""  *'"'  ^'''°  '""'•'  P'^^'^^  "^^'-  o"«  a»'^"ier,  and  appertain 

t4  s!;::ia  r  etr  :,:r.  ^^^^^ ''-'  °-  *'^°^^-'  -<'  ^^-  -^^ 

.o'd   >nro?^^r"^  '"  '  ""'■''"'''^  ""^  ««"*'^^'"^^  direction,  .nd  sus- 

H^  1  wiU   ^r  "^t'  ",'  '"'t^'"'^  '"""^  "^•^''  -'^'  P-aH.l  With  the 

r^lhTsr     /a  ^    '^'  '""*'"''  """'^  then  imagine  a  current  to 

t^e  needle  '"'"'"  '-"'^treniity,  and  determine  its  effects  ou 

7.    Why  is  a  n.agnetic  .  edio  d.;iected  by  an  electric  current? 

Of  Lllli^t?"  "  ''  '''  'f '^'^"'^  "^P^"'^^"*  ""  "-  d--«on 

npi^^*  '^!'®.®*^*^^^^®at  magnet. -Experiment  1.  ^r  i^. 
n  a  cambric  needle.     Suspend  it  by  a  fine  thread  attached  to  fs 

m.ddle  over  a  n,.g„et,  and  midway  between  its  poles.     The  need 

Trr.n  r"  •  """"^^r!^^"^  ^^^^^  ^  P-'«o"  P-aHel  With  the  mag  .' 
The  magnet  exerts  a  directive  influence  on  the  needle.  Remove  the 
vnagnet,  and  the  needle  takes  a  northerly  and  southerly  direcUon 

I)  you  carry  the  needle  all  over  your  town  or  State,  it  will  still  main- 
am  fus  direction.     Something,  like  the  magnet,  everts  a  d    eXe 
influence  on  the  magnetic  needle.  uiiccuve 

Fig.  160. 


E^jperlment  2.  Place  the  needle  once  n.ore  in  its  original  position 
over  the  magnet,  and  gradually  move  It  fron.  the  middle  toward    one 

of  the  c  nteTif ";  '  ""  "^^^'^^  '''''''  ''  ^^  ^"••^-"*'^'-     ^*  ^'^her  si"e 
of  the  center  it  dtps;  if  it  is  nearer  the  N-pole  of  the  bar,  the  S-  oi 

dips,  and  conversely,  as  shown  in  Figure  160.    If  the  needle  Is  pro,    :  v 

supported,  the  dip  increases  till  at  the  poles  the  Inclination  is  90° 

If  a  magnetic  needle  P  .  suspended  is  carried  to  .;  ,  nt 
parts  of  the  earth's  sia-iu..,  it  will  dip  as  it  a^  ^aohes 
the  polar  regions,  and  is  only  horizontal  at  or  near  the     ■   h'^ 


THK    KARTH  A   IVFAGNET.  £43 

need  to  ,.  J  the  N  "       o.a  ^if  T    '"  ^'^'-r^^' ''"^ -"^ 
Like   e,.ets    a.   eo.. ^ttti'u^r^^'^  "^^^^  ^"  ^-^-^^- 
o    -ke  causes.     These   phenomena   are 
just   what   we   shonhl   expect   if  (as   is 
very  improbable)   a  lu.ge  magnet  were 

u-ust   through  the  axis  of  rotation   o? 

he  earth,  as  represented  in  Figure 
161, -having  its  N-pole  near  tlie  S 
geographical  pole,  and  its  S-pole  near 
the  N  geographical  pole;  or  if  (as  is 
more  probable)  the  earth  itself  is  a  magnet 

plate  of  glass.    Sift  over  "'S  o'ametei.v     Place  it  beneath  a 


Fig.  162. 


the  glass  fine  iron-filings, 

as  ill  Exp.  2,  p.  28.  Geutly 

tap  the  glass  a  few  times, 

so  as  to  agitato  the  filings. 

Once  in  motion,  tliey  ar- 
range themselves  in  lines 

radiating  from  either  pole, 
forming  graceful  curves 
from  pole  to  pole,  as  rep- 
resented in  Figure  162. 
These  represent  what  are 
called  lines  of  magnetic 
force.    They  represent  the 

resultants  of  the  combined 
action  of  the  two  poles. 
Now  carry  the  little  mag- 
netized cambric  needle 
aroundthedi.sk.  It  follows 
the  lines  of  magnetic  force 
as  mapped  out  by  the  fit- 

lugs,   always  assuming  a  ^ 

position  tangent  to  the  magnetic  curve,  as  shown  in  Figure  162 

It  is  evident  that  the  space  arouud  a  magnet  is  the  «eat  of. 


ftll 


244 


KLKCTlilCITY   AND   .MAGNETISM. 


f 


lii: 


peculiar  influenco  ;  this  space,  extending  as  far  as  the  inagncr 
exerts  any  efreet,  is  culled  the  magnetic  field.  The  hist  experi- 
ment presents  a  true  exhibition,  on  a  small  scale,  of  what  the 
earth  does  on  a  large  one,  and  thereby  presents  one  of  many 
|)henomeua  which  lead  to  the  conclusion  that  the  earth  is  a 
magnet. 

§  192.  Magnetic  poles  of  the  earth. -It  will  be  seen 
that  there  are  two  points  where  the  needle  points  directly  to  the 
center  of  the  disk.  A  point  was  found  on  the  western  coast  of 
Boothia,  by  Sir  James  Ross,  in  the  year  1831,  where  the  dipping 
needle  lacked  only  one-sixtieth  of  a  degree  of  pointing  directly 
to  the  earth's  center.  The  same  voyager  subsequently  reached 
a  point  in  Victoria  Land  where  the  opposite  pole  of  the  needle 
Iack(!d  only  1°  20'  of  pointing  to  the  earth's  center. 

It  uill  l,e  soon  that,  if  we  call  that  end  of  a  magnetic  needle  which 
pom  s  north  the  N-pole,  we  must  call  th.-rt  magnetic  pole  of  the  earth 
which  IS  in  the  northern  hemisphere  the  S-poIe,  and  vice  versa.  (See 
iMg.  102.)  Hence,  to  avoid  confusion,  many  careful  writers  abstain 
from  the  use  of  the  terms  north  and  south  poles,  an<l  substitute  for 
them  the  terms  positive  and  neyative,  or  marked  aud  unmarked  poles. 

§  193.  Variation  of  the  needle.  —  Inasmuch  as  the  macr. 
netic  i)oles  of  the  earth  do  not  coincide  with  the  geographicll 
poles,  it  follows  that  the  needle  does  not  in  most  places  point  due 
north  and  south.  The  angle  which  the  needle  makes  with  the 
geographical  meridian  is  known  as  the  angle  of  declination. 
Ihis  angle  differs  at  different  places. 

Experhnct.  As  Columbus  found,  we  can  easily  flud,  the  decUna- 
tion  at  any  place  as  follows  :  Set  up  two  sticks  so  that  a  string  iolniu- 
them  points  to  the  North  Star;  the  string  will  lie  in  the  geographical 
merRlian.  Place  a  long  magnetic  needle  over  the  string;  the  angle 
between  the  needle  and  the  string  is  the  required  declination.  If  great 
accuracy  is  required,  allowance  must  be  made  for  the  fact  that  the 
star  IS  not  exactly  over  the  pole,  but  appears  to  describe  daily  around 
It  a  circle  whose  diameter  is  about  4°, 


VARIATION  OF   THE  NEEDLE.  245 

Let  A  (Fig.   16.3)   represent  the  nortli  magnetic  pole    an.l  H 
the   north  geographical  pole ;  it  will  he  l^Z 

«een  that  there  is  a  position  in  which  the 
"oedlewill  point  cine  north.  A  line  pass- 
ing around  the  earth  'brough  the  two 
'"^ignetic  poles,  connecting  those  places 

where  the  needle  points  due  north,  is  -^^_^_. 
called  a  line  of  no  variation.  On  the  min  Plot  tt  •.  •" 
marked  0.  Lines  east  and  west  of  thf,  r  ^^  f  ""  '*  ^' 
parallel  with  it,  represent  liZ  of  '"''  ""^  '^Pi^'-^-^'-'-Hv 

in  North  A  ;*^P^<^sent  lines  of  equal  variation.  At  places 
in  iNorth  America  east  of  this  lin^  iu  i,  pt'tn  s 

iiKe  an  island  or  cape,  but  are  constantly  chanrino-     ti,. 
pear  to  swing,  somewhat  like  a  nenttalnm  T„       *'    J  ,  ^  """ 
westerly  direction,  each  swing  roquTrtot  ^""tariesl'"    "ir"' 
Tl,e  north  magnetic  po,e  is^no^  onTJ^Z^^S^t 

stances  should  partake  of  its  magnetic  properti  f  dctbn" 
oxraes  ot  this  metal,  possesses  more  or  less  magnetic  oowcr 

trnZ^s  w ''™'''  """"•'"  »'^-'«.  '»'j-tingirtr:m 

irom  the  artificial  magc<-'.s  of  steel. 

fhf  ^M  ^^""^^  °^  '■  • '  ^^^^'«  ^lagnetism. -The  cause  of 
the  earth's  magnetism  is  not  known.     The  thoorv  -  i 

electro-magnet  in  virtue  of  currents  "flowing  ^^^^undTne  "  T 

surface,  from  east  to  west,  explains  all  tl  e°  eZs  thlt    t"n 

duces  ou  the  magn<  'v.,  needle      T5,.t  wi../      7        .  P'"''" 

g"  -  V  uteuie.    uut  vfhut  sustams  these  electric 


4ii 


246 


ELECTlilCITV:   AND   MAGNETISM. 


¥i 


source  ot  the  earth's  magnetism.     Those  who  adopt  this  tlieorv 
generally  regard  the  terrestrial  .  .ruut.  .s  IkernJelecMc 

certhllf  Ltrh  r"'  "r"  '"  '''''''''''  ""  '"^""-^^^  r^'-tion  that 
ne  K  "  •  In     1  t    ''";'       '   '""''   '°"^"''°°   ""''   ^^e   earth's  ™a^.. 
neti-,ni     In  18o9  two  observers  remote  Irom  eacl,  other  saw  si.n,^ 
taneously  a  bright  spot  break  out  on  the  fuee  of  the  sun      hosel  at    u 
was  oalv  nve  minutes.     Exactly  at  this  time  there  was  a  "eue ml 
t.n-b.nce  of.  ma,M.etic  needles,  and  telegraph  wires  all  over  the  wor  J 
vore  traversed  with  so-eaUed  eartk  currents.     Telegraphers    eeeivel 
shock.,  and  an  apparatus  in  Norway  was  set  on  fire.    These  phenomen 
were  qn.ckly  followed  by  auroral  displays.     S.>n.etinKvs  teleg  rhTa  e 
worked  by  earth  cu.xcnts  alone,  without  any  battery  in  the  S.      ' 

l^f?'?^''^''^^  ^^°^^^^«  °^  ^^  --'^    and  magnetism. 
-Artificial  magnets,  including  l)ormanent  magnets  and  electro- 
i^u^gnets,  are  usually  made  in  the  shap-^  either  of  a  straight  bar 
or  of  the  letter  U,  called  the  korse-skoe,  according  to  the  us" 
inade  of  them.     If  we  wish,  as  la  the  experimct^  already  d 
scribed,  to  use  but  a  single  pole,  it  is  desirable  to  have  the  other 
us  far  away  as  possible  ;  then  obviously  the  har-magnet  is  most 
convenient.     But  i"  the  mapnot  is  to  be  used  for  lifting  or  l^h 
ing  weights,   the  h  .  .,o-shoe  form   is   far  better,  be-all 
attraction  of  both  poles  is  conveniently  available 
and   becr.i.e  their  combined  powe,   is  more  than 
twice  that  of  a  single   pole.     This  is  due  ^o  th.> 
reflex  influence  of  the  poles  ..>  one  another  throu<rh 
the  armature.     Magnets,  >vhen  not  in  use,  ou-Ii 
always  to  be  prote-       by  'umatures  (A,  Fi-.  1G4) 
of  soft   iron;   for,       ,tw      landing    the   coercive 
power  of  steel,  they  slowly  part  with  their    nague- 
tism.     But  when  an  armature  is  used,  the  opposite 
poles  of  the  magnet  and  armature  being  in  contact 
with  one  another,  i.e.,  N  with  S,  they  serve  to  bind 
one  another's  magnetism.  .>    ^  vc  to  uiuct 

Thin  bar«  of  steel  can  h,  more  thoroughly  magnetized  than 


J 


Plate  IT. 


M. 

>  the  sun  as  the 
idopt  this  theory 
no-electnc. 

mate  relation  that 
the   earth's  :'nag- 
other  saw  siinul- 
n,  whose  duration 
'as  a  general  dis- 
U  over  the  world 
fraphers  received 
riiese  phenomena 
es  telegraphs  are 
u  the  circuit. 

d  magnetism, 
ets  and  cleetro- 

a  straight  bar 
ing  to  the  use 
nts  already  dt 

liave  the  other 
uagnet  is  most 
lifting  or  hold- 
*,  because  the 
ntly  available, 

is  more  than 
is  due  to  tho 
iother  through 
in  use,  ought 
(A,  Fig.  1G4) 

the   coercive 

their  nague- 
l,  the  opposite 
iug  in  contact 

serve  to  bind 

^etized  than 


fifi 


I 


!l 


ill 


BIAMAGNETISM. 


247 


b)   ..  Ic,  with  their  corresponding  polos   turned   in   the  same 

^tro^r  xr  ""^ti  '""'-'''-^  ^  -^^-  p-^-^'-i  Xe 

IS  the  result.      I  his  is  called  n  co/»^,o««cZ  «i«f7„eL     i„  .^^^  ^_ 
central  ones;  so  a  steel  tube  makes  very  nearly  as  stron-^  a 

srtter ' "'  ^' '''  ""^^  '^^"^^'^"•'  -^^  ^^  --'^  '^^'^te;:ha; 

§  197.    Diamagnetism.  _  Resides   iron   and   steel,    many 
otlu^r  substances,  and  possibly  all  substances,  both  in  the  iTou  d 
and  gaseous,  no  well  as  in  the  solid  state,  are  more  or  les    su 
cepti ble  to  magnc-tie  inflnonce.     Conspicuous  amon.  these  are 

kind.     A  small  bar  of  bismuth  suspended  between  the  poles  of 
.  Dowerful  electro-magnet,  instead  of  being  attracted  is    epe  led 
1)      he  poles  of  the  magnet,  as  shown  by  its  takin^  a  no  it  on 
w.  h  Its  longest  axis  at  right  angles  to  a  direct  line  beleen    h 
poles.     Substances  which  behave  in  this  manner  are  caTled^^a 
magnetic,   and  they  are  siid  fo  nln.n  f.  , 

botwpon  \h         1  o  ,  P      ""  themselves  equatorially 

between  the  poles,  as  iron  and  nickel,  are  called  paramagnetic 
or  simply  magnetic.  '"-agneiic, 

Paramagnetic  liquids  placed  in  a  watch-glass  between  the 
poles  become  heaped  np  at  the  poles  and  depressed  in Te  oen! 

iTquidl     Tho      'T"'l  f""™'"''^   ""'''''   "'"^   cliamaguetic 
liqinds.     The  magnetic  behavior  of  gases  may  be  learned  by 

■nating  soap-bubbles  with  them,  and  noting  Uie  direction  of 

1  eir  distension.     Alcohol,  water,  nitrogen,  and  carbonic  acid 

are  diamagnetic.     Oxygen   is   paramagnetic.     The   only  snt 

s  ances  whose  magnetic  properties  can  be  shown  without  extra- 

oidmary  apparatus  are  iron  and  its  compounds. 

§  IDS.    Magnets  not   sources   of   energy.  -  Pernetual 
motion  seekers  are  easily  led  into  the  error  of  snpposingThlt  in 
the  magnet  they  have  an  inexhaustible  supply  oT  energy  jbl^ 


III 


248 


KLECTEIGITY  AND  MAGNKTrSAf. 


«  very  little  study  will  serve  to  exhibit  tho     .    "     . 

e>ror.     If,  for  instance,  we  bri.i.  .  n •  f     .       ^-''a'-aoter  of  the 

f  i«  att-ted,  and.  if  ^Uo.^rtV  n^ ^^/t^.r''''  ^  "^=^'^^^' 
force  of  attraction  will  do  i  c<^vt.u  ^  '^  ^^^gnet,  this 

another  piece  of  iron  sti  ar^  o      rZt     ^^n*     ''^'^  ^"^^ 
-eted,  and  a  certain  an.ount  ot  wo  kt   .',,'"  f  ^  "'"  ^^  "^^- 
less  amount  than  that  done  in  til  fit  P«'-formed,  but  a 

operation  until  the  n.a  n      no  lo.     "\;*"*"^^"     ^-^^"""^  the 
J-s  done  a  definite  an^oj  .^k  :;:^tt;  """  '"^  "^^'^^^ 

more.     To  restore  it  to  its  o ,,       , '  ^  "^'  '^^^^■^'''  ^^  ^^^^ng 

allthepiecesof  iron;  "nt';:'  .^"''''^'-'    ^  '""st  remov^ 

nal  work  exactly  eq  , a   1         .''•'•'" '"''^^^'^^'^^''^  «f -^ter- 
magnet.  ^   ^        '^   *''^^'   ^''g'^^Hy  performed   by  the 


XXXH.     MAaNETO-KLECTUrc  AND  CURREXT  INn.CTION. 

a  magnetized  steel  ro<:  i,,,o  th.  c         t /V'^"-      ''^  ""'  ''"''^'^l^'  thru.st 
Fig  ,e5  ^  ,  ^^  '"^'  "^'"^''"^"^  '"^ve  you  that  a 

^i.-^65.  •  '-"^  Of  e,.,etrieity  is  i,K,ueecI 

'"     I"'  ''^■'■-^••^     l^o^'s  this  current 
;;"'t""K-,  oris  it  only  uKMuentary? 

t2>iK-klyn.u,ov(.tlu.„,afr„et.  wi.at 
i«  tlie  result  iu  this  ease?  Re- 
peat the  experiment.  U'lien  tlie 
magnet  ai)proae].es  the  eoil  wliat 
is  the  direction   of  the  induced 

current  as  coinparedwith  that  of 
the  aniperian  currents  in  tlie  ma- 

net  as  represented  in  Figs.  ir.()  ami 
1'"-^  ^Vhat  is  tlie  direction  of 
the  induced  current  when  tlie 
magenet  is  withdrawn?  if  you 
rectly  you  will  see  that    in  th.  fn.  '''"*''""'""   ^^'^'^^«    <iirections    eor- 


■acter  of  the 
ar  a  magnet, 
^'ignet,  this 
Take  now 
'O  will  be  at- 
I'med,  but  a 
'ontinue  the 
the  magnet 
'^i'  of  doiujjf 
ust  remove 
fe  of  exter- 
»<?d   by  the 


LTCTION. 

nt  1.    Con- 
ckly  thrust 
yon  Unit  a 
i«  induced 
Ids  current 
lo'iiontary? 
met.  Wliat 
a,so?     Ke- 
WJien  tlie 
foil  wliat 
e  induced 
Ml  that  of 
II  tlie  niaif- 
•s.  Ififiand 
oction  of 
vhen    the 
If  you 
ons    cor- 
ue  to  op- 
»gs  them 


MAGNETO    AND    DYNAMO    ]V[ACHINES.  O49 


Kig.  106. 


Fig.  16 


direction  must  resist 
the  force  that  sepa- 
rates them.  Hence, 
the  energy  shown  by 
the  electric  current 
has  heen  generated  at 
the  expense  of  mechayi- 
teal  energy. 

E?' peri  me  lit  2. 

I'lace  within  tlie  coil  ^.,._^^ 

a  core  of  soft  iron,     Wave  back  and  forlli  over  one  evt..      •,        ~~ 
->-■  one  of   the  poles  of  a  povve.-fu,  ha,-      "n.t       N, "  "n     .  T 
expernnents  with  the  opposite  poh-  of  the  u.a^';;!        AVh- 1 '        ^         '" 
nemena observed?     Are  they  such  as  v..,,  ^^ ''«it  are  the  phe- 

would  expect?     Wliy?  "  Fig.  les. 

§  200.     Magneto  and  dynamo 

machines.  -  If  the  pennauent  mao- 

nut  is  stationary,  and    tlio    clectro- 

iiicignot  i.s  moved   back    and    (brtli, 

the  1-e.siilt  is  the  same  a.s  when  the 
m^^gnet  was  mo^ed  and  the  clectio- 
liiagnet  was  stationary.  Machines 
constructed  for  the  purjjose  of  gener- 
ating electric  enirentsin  this  manner 
are  called  maijncto-electrkal  nmchmen. 

Fi«:.  Ki.S  will  isjive  a  general  idea  of  the 
construction  of  the  simpler  kinds  ot 
magneto  machines.  N  S  is  a  permanent 
compound  horse-shoo  magnet.  K  v  are 
coils  containing  cores  of  soft  iron  cim- 
nected  by  the  back  armature,  C  C    the 

whole   constituting  a  sort  of  armature  -— 

to  the  permanent  mairnet.     The  brass  -.vir    r.  i^   •      ■ 
with  the  back-armature   C  C  l.hT  ,        '.      ^  '  '"  '■'^'"*'>'  ^•""'«'fted 

Of  the  crank,  A.  .j^,!;^'::  '^:^2:^;:;^rT ''  -'""^ 

the  crank  to  be  turned;  duriuL'  the  fi,  .  I  '^'"'''  *'"J''^"'^^ 


k 


250 


m 


ELECTItlcITV    AND   MACJNETISM. 


in  opposite  directions  through  Cve  LaT  T'""''  '"^^  "«^  «-- 
other,  but  may  have  a  common  cUreXn  ar  ,;"■;''  "'"''""''  """^  ^"- 
of  double  the  electro-motive  fo  'rt^t \2  '^^^  ^  T '"'' "  ^"^^^"^ 
ho  ix.  During  the  second  quarter-revaTutlontlo  oof '""'''  '"  '  ""^'^^ 
other,  and  tlie  elTect  ivo.ild  be  to  rcverlH  ^    ^^  •'^PProach  one  an- 

the  cores  also  chan.^e  as  they  are  now  .'  "'^?"•^"^ '  l^"*  ^he  polarity  of 
poles  Which  they  are  app  rjhi"    a "d     "f    >',"'"  ""  '"'"^'"^  °^' he 
rent  to  flow  in  the  same  direc   "t'as  t  d  I  h  r     '  '''"^'  '^^^'^^  ">«  «»-■ 
revolution  there  is  a  reversal  of  cnL    /        f*""'-    ^'  "^«  «"''  ^^  ^  I>alf 
this  point.    The  result  KtltdS".;"    "  "''^^  '"^  "^*  ^'-"^^  ^^^ 
rent  half  of  the  time  in  o  ,e    irecSnfn  ,  rTr'r"'"*'""  ''''''  '«  ^  '="- 
«itc  direction.    I„  order  to  secure  'con  .         "'  "'"  ""'^'  '"  "'^  «PP«- 
a  current-reverser  I,  or  .::":    ,    anT Nllirr. '",  ^r  '^'''^' 
i«  so  arranged  that  during  one  hah  o     1  l  f    ,'  ?       ''*'  to  the  axle, 
connected  with  G  and  n  ^vith  li        i I  ,         '•^•volution  of  the  axis  m  is 
nected  with  II  .„„  ,  n^  n',    "',  .f  1   r'''V'''  """''  '''''  '«  '«  -- 
rents  in  the  helix-wire  nl  wc  1  „  1  ''"' '''''  ''^^'^'  «>f^'rnati„g  cur- 

".'  the  wires  G  H,  wlddr  T/  "  rV^m;T. '''  '"  "'^"  ^"""^'  ^"^-^'o" 
circuit.  ^owHL,  must  l.o  coiuiccted  to  close  the 

Each  of  the  two  currents  produced  In  n  c     , 

1  ro(uiu  u  In  a  single  revolution  has  a 

'"''  '""  "'••'ximum    point,   or  point  of 

Kreatest  intensity,  when  tiie 
cores  are  nearest  the  poles  of 
tlio  magnet;  and  a  minimum 
point,orpointofleast  intensity, 
when  they  are  farthest  from  the 
poles.       Between     these    two 

points  the  current  is  constantly 
Kioning  or  diminishing.  It  is 
apparent  that  such  a  machine 
fc'ives  not  only  an  intermittent 
current,  l,ut  one  that  resembles 
a  succession  of  waves  or  a 
Ntream  produced  by  the  strokes 
of  a  i)ump.   alternately  risin-' 

purposes  for  which  electricity  is  employ^,  Tuf      ""*    '"^    '"«^'* 
current  should  be  continnou/n,.,,  f.   /'    ^    \1    ''  '"'P«rtant  that  the 

Illustrate  the  principle  by  wh'"i    tl  ir'u'"'        f' "  ^''''  '""  ^'^^'^  *« 
Gramme  machine.  ''  *'  '"""'"'^  '"  "'^  widely-knowa 


MAGNETO  AND  DYNAMO  MACHINES.  251 

The  armature  ns  consists  nf  a  ..t^™  „ 
Irou  wires  (better  sl3n  nil /l^?^™^°'f  °^  ''  '""^^^^  ^^  ««f' 
an  eudless  coil  of  Te     T If  wi  •!  in""'""'''  '^  "'"^^  ^'^  ^"'^"^"^ 
coiIs,theln.vvireofZu„ite^to  2     T'-''"'  ''  ^^^  °"  '"  ^^P^'-^'e 

each  juuctiou  abra^h  w  re  fs  vdt  °       ''''  "'  ""  "'"'''  '"'  ''"'" 
-tatiou  ...    A  ho2ere'^„;;'„et\V7oni;f  ^'Z  ^^'^  «^ 

shown  in  the  cut)  is  so  placed  th^t  one  Lf  "f  tho         "•       ""'''"''  '' 
influence  of  the  N-nolo    «n,i  fi    "*' ""^  "a^^  of  the  ring  is  under  the 

suppose  tiJt?to'::r:;Lt:c-:no7«^  *'"  -'''-  «-^°'«- 

point  of  tlie  iron  core    a.  1*7.  "'"^  ''''™'^'  t''^"  every 

magnet.  Will  success^:,/,  e  on  a'proT''^  '  -f^^"  ''°'"'  «^  "^' 
points  .•  and  i'  are  the  neutral  n"ints  Tf  P''°"''  "'™'^'  ^^'"^«  '^e 
divided  at  tl.e  points  n  am  fwelfat  /  '''  ■'"'^''""  "^'^  "°^«  *«  ^« 
north  poles  and  wlj  2  ,'  ^1  Tes^e^IXr^^''  "^^"^*^  -^°- 
the  two  mutually-facing  pole  on  e  ther  s  le^h  A  '"'  "''"'''''■  '" 
must  be  in  opposite  direction.     ""''''  '""^'  ^'''^'  Ampcrian  currents 

diagram  in  th  1  gU  of  w  " von  ,7  ""  '"•"'"'  ^'"^^  ''^  ""«  '^-^ 
the  generation  of  induce  '.^rrts  win  ^T,''"''^  '^'^^'^'^  '''^^'^'-S 
ring  armature  rotatetth    CO  rs^on^^^  '""  ^/^^^  ^''^^  ^  "- 

of  the  ring  will  induce  cunvnt,  i    tf    ^  "'"  "^  "^"  ^"'^"^^d  poles 

the  coils  Which  afa^y  give  n  om  ntV"-'  ,"  ""'  "  '""'"«'•  *^"'  -" 
the  magnet  poles-  L   he  Wh  V"  "'"  '''"'""'^"^  "^^*  ""'^  ^^ 

^li.-oction.     Similari;:C:emTctl;rrer  !.^  ^^ 

approaching,  or  immediately  receding  fZ  he  South  no,  '"^'''''^ 
same  time  traversed  by  a  current  nf  ti  P'^'"  ^"'^  ^*  "'« 

is  that  currents  in  the  lovver  h^f  /  "  ^^'^^^^'^^  ^"^««t'^»-  The  result 
and  in  the  upper  Li  //Z  poiu  „  S  r'  ""  ^ '"*  "^  "^  *"«  ^-«. 
from  these  points  are  oZ    th.l     '         t    f^  ^'  "'^  ^'^'*^*°S  ""^-wires 

nuently  op/ose  ancTuVuSr  eZire^'tutTf  "r"  "T  ^°"^^^- 
«^'  are  connected  by  a  wire  L  we  shnlliU  ^^'""^^  "^  ^»'' 

;;;.  currenc  flowing'throu^h'C^^r?  ^^^  IToT  ^ J^'^l"^""- 

Xf  tct:::r:r^  f  --ror:pper;:r :! 
co.;;ntconn:tS::i«;\;t^rSersr;t^^^  ^^^^^"""^-  '^ 

inducing  or  the   so-callod  /;  / ;  ^        extensively  used  as  the 


252 


ELECTHICITY  AND  AfAGNETISM. 


^  ~;:  t:x^::-:zr::i:  s-  --  -  anna.. . 

-inch  «oft  h-on  ahvays  ret^Uus  Xr   t  1  "    ,    '""'  "'  "'^  '"'^^«etis,n 
at  flivst  a  M-eak  a,.Tc.„t  in  the  wire  of  t  .  T  '"'•^'^"^'^'■^^-O  mrtuces 


i"  ig.  iey  fc. 


?Hl 


;'"'  «''1<I  ma,-r,„.t,  and  nmif.,oti/es  th,-  ..,.., 

A  ami  n,  „„  „„k„  ,„  „„  ,,,„„„™';;;;, ■;'"'■■  «■■".««„.„.  ,,,0  d,„L„„s' 

'"  ' iniiati.ro  wilua  11.  "  ,vt„,., ■.:..'.;;'    ;'  ''?  '"'«"  "»  many  iu|.|,» 


r»te  of  i-evoUitlf 


I  ; 


f'»-  Which  niJl 


I  the  armature  Is 
tJie  magnetism 
'ictized)  induco.v 
t  as  a  portion  of 
>iigh  tlie  coil  of 


.  i6a  b. 


CUHREST  INimcTrON. 


re  stroiiglv, 
yroacljc'sju 

isod  (§  201) 
L-  tlyuamos, 
many  turns 


253 

ffiA-e  the  greater  E.M.P  ?    t..  «« 

f '-  coil  makes  it  necc.;ary  to  ^"1//"'  T''"'  "^  ^""'^  '"  the  anna, 
•ted.  What  eflect  has  tlus^,^!  n T  '''*  ""''''  '"'''  ^"^'  ^P-^"''  is  li^- 
cnrrent  must  traverse?  The'  doh.  .  uT'  "'  "'^  ^''''^'''t  the  induce, 
coils  Of  the  fleld-magne  ;  r  ;  :'''^r'''''"^'''^^'™'^*"--on"S 
c."t  The  fleld-magnlt  .oi  „  ^^  '"r''  ""^^'- ^'^^  "^  the'ci" 
.->.netunes  arranged  in  nn.l.ip,.  a  ,  t  U  n"^  ^^  "^•'^*"-""«  ^^'re  are 
-nes.  This  arrangement,  L  S  I  ho  '^  v"'  '"''  '^'""''^''-^  '" 
Icpens  upon  the  Mork  for  whic-h  tl  '  nln  "'""^  ^'  ""-'  '"-"lature, 

■''^^-^.ne  Wire  has  a  very  high  r.!^  ."l  ;;;;,;; ,f-'^-^-  U  the  work: 
"•th  many  t,„-„s  of  fine  wire  or  wit     .wt  "  '""'"''''"''  ""'  ^^""'"^ 

constructing  dynan.os  care  nn.stT.  /  ?  'r''^  "^  — -  -ire?  m 
«i/^e  that  the  current  passing  t,  , '^S  /V"*'''  ^'^^'■J' ""•«  of  such 
«peedslull  not  be  sufficient  to^u^:,;^^^^^^^^^^^^^  the  dynamo  is  at  f  uU 

§201.  Current  Induction. -If   i„  ♦,        •  . 
m  magneto-electric  induction  (§  vm     '  "'' '^'''^''"■'^^  ^^'PeH.ncnt 
battery  is  substituted  for  the  Lnn.:  \  ««""ected  with  a 

«ame  results  are  obtained  an  wit    tl  rr  ,r'''"r^;  ^'r '-'^'  '^- 
to  expect  the  same  results.     (Win         t"     ^'!'^'''^^  ^^  ought 

^"'00      Ihe  wire  A,  Fig.  170, 


PiK.  170, 


tlirough  which  the  battcrv-currenf  ,  i      . 

case  as  tl,«  ..;...,,.  ,. ..-^  ''"'''"*  '^"-.^illateH,  in  known   m>  f..{, 

or  mdt^cm^  cnrrevt.     The  wh.    H     ""'"'•>'-^''"-''«"t  the  primary 

currents  circulate,  is  called  the  ./      ;  ""^     '"'^'''^  "''^^  "'^^"'^«d 

fl'at  traverse  this  wire  are  frc4en«vtj  T'''  ""^  '^^  "'^^«"^« 

frequently  called  ^econrfar^  cum/i^. 


^|t 


254 


EI.ECTRlCiTV  AND  MAGNETISM. 


Ill 


Ml 

il 
■,'i 


It  will  be  observed  that  in  nil  4-u 
relative  motion  between  a  cond  1?  7"™"^*^  "^  ^^^  ^ 
(rnagnet  or  current-bearing  TkI  2)^^^  T^"^''^"^  ^^^^ 

flows  onl^  during  the  continuance  ot"  ;elti''  "'■ ''''''''''' 
cate  measurements  have  proved  hat  nr^  T*'^^"'  ^'^^• 
lucluced  electricity  transmittecl  t  T  .  "**"'  ^"'^^"^'^^  ^^ 
tl'e  total  quantity  of  ehann  V.  '''"^"''"'"  "^'^'^^^  ^n 
oa  the  cime  occupied  in^rchange '^I  "'""^'  ^"^^  ^^  ^'  "^» 
tlic  more  rapid  the  change  thf  mnrJ-  /  ''''  '*  '^  •^^''dent,  that 
t-.y  current ;  i.e.,  the  S; te.-  mn  .?'  "^"''  '^^  ^^^  ™««^-- 

-"t  flowing  at  tl.  moCt      clb         "  r'""^  ^' "^  -•- 
Ohm's  law,  rememberin.  thlt  the       " /'  ""  ^^''*^"^«"*  ^^^^ 
circuit  is  constant,  we  derive   hff  H        '"''  "'  '^^  ^^'^^"darv 
In  a.,  inauced  current,  Z  EMp"'7  ''''  '^P^^'^'^"^  'aw^ 
^^onal  .  ae  ra^iaUy  of  tUe  r^<^^^.::;^Z ::T^ 

found  that  making  and  breaking  (ri.?rr  ^''''^'"  ^"«  '^"«r.  it  Is 
.  arfng  and  stopping  a  primary  cu  ret      '  „ ""  ""''"^'''y  '^"'-^nt,  ^•.e., 

'.try  wire.     Indeed  this  process  L  eviden  '  ""''''"''  '"  "'^  ^^con^ 

"'  theory  exactly  the  same  thinl     11  ^  '""'''  '^'  ^'^'"'^  thing  (and 

with    unbroken    circuit,  Jm  f,  ^1'"^"?  "'^  P^^™-^  cond'ucto"' 

would  be  zero,  into  the  ^econlrTcilrthf'rr  "^""  '*«  -«- 
a  very  brief  time.    A  reversal  of  t ,  "''^^''^  ^^^"««  occupying 

«Pond  to  breaking  the  pr^arT  il  "  C  7""'  ^^''^'^""^^  '-- 

§  1««,  enable  us  at  once  to  predi™    dil.r'''"'  '  "'^"^"^"'^  *"  ^xp.  i. 

"  aTVT'  ^-"-^ate  the  two  clsfs  tlfus  !^"'  ^'  ""  ^"^"^^^  — t. 

0/  «Ae  /)nwaj-y.  ""^^"^  ^"^  ««  op/Jostie  f?eV<»c<w«  fo  that 

<Ac  jDnmory.  ""^"  fi«newf  has  the  same  direction  as 

secticu  ldnTl^^^!^.^''t~'^^'^  conclusions  of  the  preop^ing 


we  have  a 
cing  body 
electricity 
oil.    Deli- 
iai)tity   of 
spc-uds  on 
not  at  all 
dent,  that 
e  momea- 
'  the  cur- 
lent  with 
econdary 
ant  law: 
'  propor- 
\t. 

econdary 
tter,  it  is 
fent,  i.e., 
le  secon- 
i"g  (and 
nductor, 
5  nction 
icupying 
y  corre- 
I  Exp.  1, 
"urrent, 

'lated  in 
!  to  that 

'nt  1%  a 
'Hon  as 


(firlir 


it  any 

i  COQ* 


INDUCTION  OF   COILS,  255 

ductor  gives  rise  10  a  current.     But  it  is  evident  that  in  «    •     , 
wire  every  portion  must  bo  considered  as  a  neil  ''°^ 

tor  with  respect  to  everv  other  nZlt^  "^'ghl'onng  conduc 

be  no  change  of  eU^Z^r^^  T^'r^r^  '''' 
panymg  induction  phenomena.     If  wc  s 'ddcnlv  '  ""' 

the  current  does  not  abruptly  assume  -tsla^S     T  ^  '"'"'' 
there  is  a  current  indnoJirf^t  mtensity,  because 

-0.  as  to  :ztTJXT.:r%:T  'r^r " 

circuit  be  suddenly  brotpn    fK  '  *'^°'  '^  ""  ^^o^^d 

--ion  Of  ^i^z::^:.^^:^:^:-;^  ^^  r 

^ero.  These  induced  currents  are  often  for  L  f^^^'^f  ,.*« 
tinction,  called  extra  current.     Or?  '     „  ^^^  '^^^  °^  ^'•«- 

ductor  are  kept  close  tolttrh"?' ''  '"  ^'^'^  "^"^^  '<^^- 
or  a  spiral,  thl  ^^ ^^S^ ^:::^' ^]:^-J^->  ^  helix 
direct  extra  currpnf  m„cf         '''''^®^s«d.     It  ,s  evident  that  the 

the  latter  is  subtracted      Thk  T   t  ""*  ''""""'y'  «■'"'" 

on  breaking  a  st™.  current  ,„,  ""T  "'  ""=  ""«•"  »'-* 
or  Shocks  fxpericne'ed  n  „  t  thV  S*'*'"^'^"'  '*'»'^ 
«peri„,ent  illustrated  b/ pZ'e  fyo  P;TV'™"  '"  '"" 
introduced  into  a  heliv  the  ItZ  „  .  ""'  "■°°  <">''«  '« 
by  the  action  o,  the  n^^lir^Xr^Xpr"^  '""«-'' 

ooil,itisevidentthita'J^rii;,:Xr''dV''^  ''""■^'^• 
every  tin,e  the  pri.uar,  is  n,ade  a:^  f  The  sTT''"'! 
cessation  of  AmpWan  carr,>nt,  i„  "°'""':  ^'"'  starting  and 
as  the  primarv    u   tot   .Td  ,,     """^  '"  *"  »""■«  '««"'»„ 

ment  and  cndingof  the  -i'  "'"'"'"""'■«''  "'*  *«  -nimenee- 
secondary  current  To  IT'  T'T'  8'''"'"^-  '"'»"'i''es  the 
in^  bv  hLd  "!■;  F  "  IT-."""."-"'""''  of  '"aki-g  and  b,^ak- 

constrnctio~n'of  an  a^tolllc' "t""™,''  "'''*  '"'''''^''  '»  ""e 

i.™  han,mer4  is?onnert^rwi,h7.    Tt'""*  '"'""•     ^  ^°« 

turn  connected  wZne  of  the  ,  7'  '"""'''  ^'  ""'*  '^  '" 

"'"=  "'  ""o  ternnnals  of  the  primary  wire. 


256 


r  i4 


4' 


Iff 


m 


ELECTRICITY  AND  MAGNETISM. 


The  hammer  presses  against  the  point  of  a  screw  d,  and  thus 
through   the   screw,  closes   the   circuit.      But  when  a  current 
passes  through  the  primary  wire,  the  core  becomes  magnetized 
draws  the  hammer  away  from  the  screw,  and  breaks  the  cii'cuit' 


Fig.  171. 


The  circuit  br..ken,  the  core  loses  its  magnetism,  and  the  hammer 
springs  back  and  c-loses  tlie  circuit  again.  Thus  the  sprint  and 
hammer  vibrate,  and  open  and  close  the  primary  circuit  with 
great  rapidity.  An  instrument  made  on  these  principles  is 
called  an  induction  coil. 

§  204.  RuhmkorflP's  coil. -This  instrument  has  the  impor- 
tant addition,  to  the  parts  already  explained,  of  a  condenser  Bli. 
This  consists  of  two  sets  of  layers  of  tinfoil  separated  by  paraf- 
tne  paper;  the  layers  are  connected  alternately  with  one  and 
the  other  pole  of  the  battery,  as  the  figure  shows,  so  that  they 
serve  as  a  sort  of  expansion  of  the  primary  wire.  When  the 
circuit  is  broken,  the  v-xlra  current  would  jump  across  at  b,  and 
would  vaporize  the  i)oints  of  contact,  and  form  a  bridge  with  the 
vapor  of  metal  that  would  prolong  the  time  of  breaking.     But 


THEEMO-ELECTE ICITY. 


257 


when  the  condenser  is  attached,  the  extra  current  finds  an 
escape  into  it  easier  than  to  jump  across  at  6,  so  the  vaporizing 
of  the  contact  is  avoided,  and  tlie  time  of  breaking  being  much 
shortened,  the  secondary  is  much  more  intense. 

The  primary  helices  of  induction  coils  consist  of  comparatively 
few  turns  of  coarse  insulated  wire  ;  but  the  secondary  helices 
contain  many  turns  of  very  fine  wire,  insulated  with  great  cai-o. 
The  secondary  current  is,  at  breaking,  as  we  ought  to  expect 
from  the  extreme  rapidity  with  which  the  primary  circuit  is 
broken,  distinguished  from  the  primary,  or  galvanic  current,  by 
its  vastly  greater  tension,  or  power  to  overcome  resistances. 
A  coil  constructed  for  Mr.  Spottiswoode  of  London  has  two 
hundred  and  eighty  miles  of  wire  in  its  secondary  coil.  With 
five  Grove  cells  this  coil  gives  a  secondary  spark  forty-two  inches 
long,  and  perforates  glass  three  inches  thick.  Many  brilliant 
experiments  may  be  performed  with  these  coils  which  will  be 
indicated  in  connection  with  frictional  machines. 


and 


XXXIII.     THERMO-ELECTRICITY. 

§  205.  So  far  in  our  experiments  we  have  obtained  a  current 
of  electricity  by  using  the  potential  energy  due  to  the  chemical 
afllnity  of  zinc  and  sulphuric  acid,  or  by  ex[)ending  mechanical 
energy  ;  can  we  not  also  get  a  current  directly  from  the  molec- 
ular energy  that  we  know  as  heat? 

Experiment.  Insert  in  one  screw  cup  of  a  sensitive  galvanomotc  r 
an  iron  wire,  and  in  the  other  cup  a  copper,  or,  better,  a  Gcriaan  silver 
Avire.  Twist  the  otlier  ends  of  the  wire  together,  and  heat  them  at 
their  junction  in  a  (lame;  a  dellcction  of  tlie  needle  shows  that  a  cur- 
rent of  clectricitj'  is  traversing  tlie  wire,  riace  a  piece  of  Ice  at  their 
junction.  A  deflection  in  tiie  opposite  direction  shows  that  a  current 
now  traverses  the  wire  in  the  opposite  direction. 

These  currouts  are  named,  from  their  origin,  thermo-electric. 
The  apparatus  required  for  the  generation  of  these  currents  is 
very  simple,  consisting  merely  of  bars  of  tM     different  metals 


I: 


liM 


! 


It  1 1' 

I  i 
If 


I  i  in 


258 


ELECTRICITY  AND  MAGNETISM. 


omed  at  one  extremity,  and  some  moans  of  raising  or  lowering 
the.r  temperature  at  their  junction,  or  of  raising  tl.c  tempem  ,r! 
at  one  extremity  of  tke  pair  and  lowering  it  at  L  othe,Tfor 
edectro-n>ot.ve  force,  and  consequently  the  strength  of  the  cu  ! 
the  two  "T^  ?''P^f^--'  to  the  difference  in  temperature  of 
the  two  extremities  of  the  pair.     The  strength  of  the  current  is 
dso  dependent    as  in  the  voltaic  pai,  on  the  thonno  elect  -l 
motn  e  force  of  the  metals  employed.     The  following  thermo- 
electnc  senes  ,s  so  arranged  that   if  the  temperature^  of  both 
junctions  are  near  the  ordinary  temperatures  of  the  air,  those 
.e^ls  farthest  removed  from  each  other  give  the  strongest  cur! 
rent  when  combmed ;  and  the  current  passes,  when  heated  at 
then,  junction    from  the  one   first  named  to  that  succeeding  it 

Jnd  con"  T  '''  ''"^^'"^  ^^  ''''  ^"--'t  ''  t^«  J-Ited 

and  cold  ends  re::,po,.>tively.     At  high  temperatures  the  current 
may  be  reversed  v^uxiuus 

Cold. 


.a 
pq 


03 

.a 
o 


a 

g 

O 


~i 

u 

<u 

. 

0) 

i£ 

•o 

Q, 

2 

o 
o 

3 

3 

a 


1> 


CC 


•=      2 


Heat. 


-> 


t 


S3 
<1 


HEAT 


§  206.    Thermo-electric  batteries  and  thermo-pile  -^ 

The   electro-motive    force   of    the   thermo-electric  pair  is  v^ry 
small  in  comparison  with  that  of  the  voltaic  pair  • 
hence  the  greater  necessity  of  combining  a  large         ^'^" "'" 
number  of  pairs  with  one  another  in  series.     This 
is  done  on  the  same  principle,  and  in  the  same 
manner,  that  voltaic  pairs  are  united,  viz.,  by  join- 
mg  the  +metal  of  one  pair  to  the  -metal  of  an- 
other.    Figure  172  represents  such  an  arran^e- 
mont.     The  light  bars  arc  bismuth,  and  the  dirk 
ones  antimony.     If  the  source  of  heat  is  stroncr  ■      ■ 

and  near,  by  either  conduction  or  convection  on'e  face  may  bo 


or  fowering 
cmperature 
lor ;  for  the 
of  the  cur- 
perature  of 
3  current  is 
nio-electro- 
ng  thermo' 
es  of  both 
!  air,  those 
)ngest  cur- 
heated  at 
needing  it. 
iho  heated 
!ie  current 


3 -pile.  — 

r  is  very 

ng.  172. 

HEAT 


^ 


lOLD        T 

,  J 


THKUMO-KLKCTUICITY, 


259 


heated  much  hotter  than  the  other,  and  a  current  equal  to  that 
from  an  ordinary  galvanic  cell  is  ofti'ti  obtuiii.-d.  Instruments 
conbtructed  on  these  principles,  and  uHcd  uh  a  source  of  elec- 
tricity, are  very  convenient  and  efricient  for  many  purposes, 
especially  when  a  steady  current  is  requin^d  with  st  xternal 

resistance  ;  they  are  called  thernio-electrk  hallcrieH. 

If  the  source  of  heat  is  feeble  or  distant,  the  feeble  current 
may  serve  to  measure  the  difference  of  U-niperature  between  the 
ends  of  tiie  bars  turned  toward  the  heat  (as  in  Figure  172) 
and  the  other  ends,  which  are  at  the  tt-mporature  of  the  air. 
The  api)aratus,  when  used  for  this  pur,.os(,,  is  called  a  thermo- 
pile,  or  a  thermo-muUiplier.  A  combination  of  as  many  as 
thuty-six  pairs  of  antimony  and  bismuth  bnrs,  connected  with 
a  very  sensitive  galvanometer,  constitutes  an  exceedingly  deli- 
cate  thermoscope  and  thermometer.  QiiantiticH  of  heat,  that 
would  not  perceptibly  expand  the  mercury  in  an  ordinary  ther- 
mometer,  can,  by  the  use  of  a  thermo-electric  pile,  be  made  to 
produce  large  deflections  of  the  galvanometer  needle.  Heat 
radiated  from  the  body  of  an  insect  several  inches  from  the  pile 
may  cause  a  sensible  deflection. 

Some  contrivance  by  which  heat  energy  may  be  directlv  trans- 
formed to  difference  of  electrical  potential,  capable  of  doin^  as 
much  work,  or  nearly  as  much  work,  as  tlu!  heat  itself  can"do 
is  very  much  U)  be  desired.  When  discovered,  as  it  probably 
will  be  in  time,  it  will  supersede  all  present  methods  of  produc- 
ing the  electrie  current.  In  the  thermo  pile  heat  energy  is 
transformed  iodifft^ronce  of  electrical  potential ;  but  the  contriv- 
ance is  not  efficient ;  too  much  of  the  heat  energy  is  dissipated. 


.Jiiii 


may  be 


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IMAGE  EVALUATION 
TEST  TARGET  (MT-3) 


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JA 


L25  III  1.4 


1.6 


PnoiDgraphic 

Sciences 
Corpomtion 


23  WEST  MAIN  STREET 

WEBSTER,  N.Y.  14580 

(716)  872-4503 


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;^'«-Mr»i;agaMa;aaar^^2 


260 


ELECTRICITY  AND  MAGNETISM. 


1  1       , 

If 


XXXIV.     FRTCTIONAL    ELECTRICITY 

placing  a  square  board  on  Sri  and     ^    ,  ''""^  ^^^'^  §  '''^  ^^^ 

iegs.     Let  a  person  whom  TlTZju       ^^'  *"™''^^'^'  "^'''^  «- 
^t    a    second    person?  '^^^  *^°''"  ^*""^  «"  ^^^^  «tool,  and 

James,    strike    Jolin    a  „.      „ 

few  times  with  a  cat's  '^'  ''^' 

fur.     Then    let    James 

bring  a  knuclcle   of   a 

finger  near  to  some  part 

of   John's   person,   for 

instance  a  knuckle  of 
Iiis  hand,  or  his  chin  or 
lioso ;  an  electric  spark 
will  pass  between  tlie 
two,  aLd  both  will  expe- 
rience a  slight  shock. 
The  length  of  the  spark 
shows  that  the  electri- 
city is  urged  by  a  high 
E.M.F.,  like  the  induced 


currents  of  the  magneto-machine  and  induction  coil. 


§  208.   Electroscope.  -  Experiment.     Suspend  in 

bo  near  cocb  other      «,7    ,1     °  ™"'°'"  1">«'°°«  ■™J'  lA 
timeJlthaefor  ic.hf,l°I  '      "  '""  ''°™  """'''  "  '"'' ^ 

..en.,,,  o.  t 'sr.^  r:'?„rt"or/rT',i  "°^  "■"  "■>"-  - 


.to 


electrifl- 

§  214)  by 

rs,  used  a:) 

stool,  and 


olecular 
laers  an 
at  each 
r  known 
inner  is 

Ig-  174. 


per  ox- 
li  verge, 
sbody. 


ATTRAr;TIONS  .^ND  REPULSIONC,   ETC.  261 

We  have  already  found  that  this  force  is  due  to  electricity 
Bodies  in  th.s  state  are  said  to  be  charged  with  electricity,  or 
simply   dectrijied.     Such  electrification   in   a   person   is   often 
manu^sted  by   a   divergence  of  hair  on   his   head.     Any  ar- 
mugement,  like  that  of  the  foil   just   described,   intended   to 
detect  the  presence  of  electrification,  is  called  an  electroscope. 
One   of  the   most  common  and  useful   electroscopes   consists 
ot   one   or   two  pith-balls,    made   from  the   pith   of   elder  or 
sunflower,  suspended  by  silk  thread.      If  an   electroscope   is 
brought  near  to  either  pole  of  a  secondary  wire  of  an  induction 
co.l,  a  similar  electrification  is  manifested  by  the  poles      Like- 
wise, by  means  of  very  delicate  electroscopes,  the  poles  of  a 
eCdld       "^■'  '^  ''  ^  ^^--b^ttery,  are'found  to'be  fel; 


Experiment  1.  Poise 


Fig.  176. 


^  209.  Attractions  and  repulsions 
a  flat  wooden  ruler  on  an  inverted 
bottle  or  flask,  having  a  round  bot- 
tom, as  In  Fig.  175.  Draw  a  rubber 
<;omb  two  or  three  times  through  yonr 
Jiair,  or  rub  it  witli  a  woolen  cloth,  and 
place  it  near  one  end  of  the  ruler. 
What  takes  place?  What  does  the 
phenomenon  indicate? 

Experiment  2.  Hoh;  the  comb  over 
a  handful  of  bits  of  tissue-paper. 
What  is  the  result  at  first?  What 
takes  place  in  a  short  time?  What 
do  these  phenomena  indicate? 

§  210.  Two  states  of  electri- 
city. -  It  is  quite  apparent  that  we  are  now  dealing  with  a  very 
different  class  of  electrical  phenomena  from  any  that  we  have 
previously  observed.  It  is  also  quite  as  obvious  that  we  are 
dealing  with  electricity  in  a  very  difforont  state  or  condition 
from  that  in  which  we  have  before  studied  it.  Hitherto  we 
have  studied  only  those  phenomena  produced  by  electricity 


i 


262 


ELECTEICITY  AND  MAGNK^TISM. 


E  I' 


I'  !• 


If 


When  in  motion  ;  and,  inasmuch  as  when  in  that  staf .  Jfo 

we  fl„<,  that  o,«  f,  thl'  r"!  ^.  ""'  °"  *^  *>"'"  "'««>• 

decomposition,  or  ffivinjr  shookQ      Rnf  v.     ^  "s,  pioaucing 

ehamed    vifl.  T      ,  "*  "^^  observe  that  bodies 

.31;,"'?'''^^    '''''"^^*^-   "^^^^'^•^  extraordinary 

t.om  the  attractions  and  repulsions  observed  between  parallel 
currents  (§  189).  ctvYccn  paiauei 

This  state  of  electricity  is  called  static,  in  distinction  from  the 
current  state,  which  is  often  called  dynamic.  We  have  seen 
that  under  certain  conditions,  electricity  may  change  from  one 
state  to  the  other,  as  when  the  electricity  which  had  accumu- 
lated m  the  boy  on  the  insulated  stool  passed  ^  >e  other  bov 
producmg,    in   its   current  •^' 

state,  both  illuminating  and 
physiological   effects;  and 
again,  when   a  current   is 
broken,  the  current  ceases, 
but  electricity  accumulates 
in  <^he  wire  (see  §  208) ,   We 
have  also  learned  that  elec- 
tricity  of  high    potential, 
such  as  is  most  readily  de- 
veloped by  friction,  exhib.   u__„,^^ 

s^-ifdX''\ul"r"''^;  t"'  '^''^'''  ^'^^  ^«p"^«--'  -St 

SI  jungly,    but  we  must  be  careful  (>  avoid  the  notion   that 
these  are  peculiar  to  electricity  so  derived. 

§2U.  Two  kinds  of  electrification. -Experiment  1    Rp.^ 
assail  glass  tube  into  thefoHnrepresentedbyA.Fjur^X^^^ 


ELECTRinCATION. 


268 


l''ig.  177. 


KItf.  178. 


aTitrbal  ^nT'' ''''"'■ '^''^'^^'^  ""■^"^■"^'  ^^om  tho  tube 

Juof,  and  present  it  to  the  ball.     Now,  rub  a  stick  ol'  sealing-wax  or  a 
hard-rubber  ruler,  with  rtannel,  an.l  i,re-  * 

sent  it  to  the  ball,  which  has  just  been 
in  contact  with  the  excited  glass  rod. 

Experiment  3.  Suspend  two  glass 
rods  that  have  each  been  rubbed  with 
silk  in  -,wo  wire  stirrups  (Fig.  177),  and 
present  them  to  each  other.  Suspend 
two  sticks  of  sealing-wax  that  have  been 
rubbed  with  flannel  in  the  same  niaiuier. 
Now,  in  a  like  mamier,  present  one  of 
the  glass  rods  and  one  of  the  sticks  of   sealing-wax  to  each  other. 

Experiment  3.  Make  a  pin- 
hole in  eacli  end  of  a  hen's  eg<r, 
and  blow  its  li<iuid  contents  out. 
Apply,  with  flour  paste,  tin-foil 
smoothly  to  the  surface  of  the 
shell,  and  completely  cover  it. 
With  a  drop  of  melted  sealing-wax 
attach  one  end  of  a  silk  thread 
midway  between  the  ends  of  the 
shell,  so  that  it  may  be  suspended, 
as  in  Fig.  178.  i{ei)eat  Experi- 
ment 1  witli  tlie  shell  as  with  the 
l)ith-l.all.  (Carefully  note  the  phe- 
nomeuK  in  tlic  above  experiments. 
Wliat  conclusions  do  you  draw 
from  them? 

It  Is  evklciit  (1)   that  there 
are  two  kinds  or  conditions  of 

d.clrijtm,ton;  or,  for  eonvenv-ioc,  w.  »u,„.!ti,„™  M,y  («o  kimU 
ofelecncuy;  (i)  .„at  l„ey  ne  .o  .olaW  U,  ,.„ch  otUor  a 
l^ek,n,U  repel  a-M  unlike  kUOs  „Un,c,  o„«  anolker.  The  To 
kmds  are  usually  distinguished  fro,,,  o„e  a„o,l,er  ,,v  the  names 
po.«(.««  and  ncyalue,  or,  ,„„,■„  l,ri,„v,  „« +,-  and-.  T|l 
forruor  ,»,   by  dennition,  such  as  is  ,Ievelo,„,d  o„  ^lass  wl,o. 


If 


r 


264 


ELECTRICITY   AND   MAGNETFSM. 


Il: 


rubbed  will,  flannel,  a,„i  the  latter  is  the  ki„d  develoned  od 
Beal.ng-wax  ,vl,e„  rubbed  with  flannel.  There  inorea«r 
except  custon,, , or  calling  the  one  positive  rather  tbl  the  X;: 

n..rr,';=.A;etr;raXr,r  vvLrr'T-""^  r » "-■ 

pith-ball  touch  the  ttannol      wLf  t^L        ,       .         "'"  '*'""'*•     ^""^  "^^' 
Ooekindof  electrificatio,,  i,  nevcrdeveioped  alone  ;  when  two 

cSeT ::::"'  "t^"  -'■'"  -  -'^^  "-n.'opjit; 

aeve  oped  o  ,  a  lubber  comb  when  it  is  passed  through  the  hair  ■ 
»lso  the  lend  developed  on  a  person  when  whipped  ;m  fnr  bj 
prese„tn,g  the  bodies  whose  eleetriflcation  i.  L  be       t  d  to  '   ' 
body  having  a  linown  electrification. ) 


Fig.  179. 


.-    .«  near ,.  one  e„a  ot  the  shei^'I^T^rtotrril^S 


DISCHARGE. 


eveloped  on 

no  reason, 

a  the  other. 

with  a  flaii- 
ilt?  Let  the 
ediately  pre- 
'  the  effect? 
the  electrifi- 
I  repeat  tlic 


i  when  two 
oppositely- 
•never  any 
tity  of  the 
itriflcation 
1  the  hair ; 
th  fur,  by 
ested  to  a 


265 


rg-shells, 

hi  Fi<?. 

ling- wax 


rod  excited  with  flauuel,  aud  therefore  having  -..     While  the  rod  is  i„ 

bv7sill  Jh"'  TT  "  ";^  ''"^  "'  ti.s.suo-paper,  or  a  pith-hall  suspended 
by  a  silk  thiead,  along  the  eggs,  not  allowing  it  to  touch  them.  Where 
clo  j-ou  find  the  attraction  strongest?  Electrify  your  pith-ball  negatively. 

pith-ball  to  the  eggs.  Are  they  electrified  alike?  If  not,  which  is  4-v. 
and  wluch  is  —?    Separate  B  from  A  three  or  four  inches  while  iTis 

fled  pith-ball  to  the  eggs.     Are  they  still  electrifled? 

We  learn  from  this  exi)eriment  that  without  transference  of 
e.eetncity  from  the  exciting  body,  or,  as  it  is  usually  expressed, 
by  induction,  we  may  charge  at  the  same  time  two' bodies  one 
with  4-e,  and  the  other  with  — e.  ' 

«ii^"  ^^SO^arge.-ExpeHment.  Bring  the  two  shells  oppo- 
sitely charged  near  one  another;  when  near  enough  they  exhn)it 
mutual  attraction  for  one  another.  On  bringing  them  still  neare  . 
spark  passes  between  them,  tlieir  mutual  attraction  suddenly  ceases 
and  on  testing  them  with  an  electroscope,  it  is  found  that  both  have 
lost  their  electrification,  i.e. ,  both  have  become  discharged. 

Wien  two  bodies  containing  equal  amounts  of  opposite  electri 
cities   are    brought  together,  both  become  discharged.      Durln- 
the  process  of  discharge,  the  electricity  which  was  previously  in 
a  condition  of  rest,  or  a  static  state,  assumes  a  condition  of 
motion,  or  a  dynamic  state,  as  is  shown  by  a  spark  passing 
between  the  two  bodies  when  brought  near  one  another      One 
of  the  bodies-tliat  positively  charged-is  at  a  potential  higher 
ban  that  of  the  earth,  the  other  being  lower.     When  they  are 
brought  sufficiently  near,  the  tendency  for  tlie  electricity  to  pass 
from  the  region  of  higher  potential  becomes  strong  enougli  to 
penetrate  the  insulating  air  and  establish  a  condition  of  equili- 
bnum.     In  this  particular  case  the  result  is  zero  potential  or 
no  electrification  ;  but  in  general  botl,  bodies  wouhl  be  b^ft  at  a 
bke  condition  of  electrification,  its  sign  depending   upon    the 
sign  of  that  electricity  which  was  in  excess. 
We  may  now  understand  how  it  is  that  an  electrified  body 


I 


iii 


266 


in 


;^)1 


!    f 


Bl^mTUmiTY  AND  MAfJNETlSM. 


'^ttiacts  to  it.elf  light  bodies  i„  it«  vh,'„|tv      P 
stick  of  sealing-wax,  excited  with  Z>   h.     1  ,  ^  ''  """"i^^^'  « 
induces  -f  e  next  itself  and  repels      ,  \    T^     T'  ^  ^^'"^■^''^"' 
forces  arc  in  action  between  teLTI  '     "'"•^'  "'"    ^^^^'^ 

attraction  between  the  -eof  L  >  "''"  "'"'  ^''«  P'^'-^'^-^H  • 
Pith-ball,  and  repnlst  be^t:  trr^r;;^ "'  ^  +^  ^^  '- 
the  ~e  of  the  pith-ball      Bnf  sin.    7  ^-ahng-wax  and 

«-case,ti.el.actione^:ru;e:t^^^^^^^ 

that  is,  the  opposite  ends  become  oppoL  "  1l  '.'^'""^^  P°'-^-^'- 
withthe  flnger.  Tlirough  your  bodrttf  h  "''''"'■  ^ouch  the  shell 
the  earth,  while  the  posttive  char^  r '^  ''*"?'"'  '"'"''^'^  '«  ^h-'^^"  *« 
(Explain.)  Remove  the  ^  .^r  and  i  !  ^  "  "^"^''"'^>'  ^o  the  rod. 
the  shell,  and  you  will  Had  «  a^  1    Is  Sm  wli     TV'  "''^  ''''''  *««' 

-or+e?)     Touch  this  Shell  With    L.othrhH^^^  ^'^  " 

Test  them,  and  you  find  that  tiiev  huvn  h  7  .'  "'"  '^'^Pa'-ate  them. 

It  is  evident  that  the  flr«t  si  el   be  ame   ttHn"     "'  ?'  ^'-^^^A-tion. 

.irriSrz:;.:;:;r:::;;^:;-;r 

that  the  electricity  could  not  W 1  t^  Hnl"     '     I'  \"'''^"* 
we  could  not  have  charged  the  shell      Mn.  '"•^'  "'^"'^'^^ 

alW  electricity  to  pai  reac^,;'^  ou-d     h  rr'^n^  ?^  "^^ 
conductors  or  ui.t^^ator«.    A  bodv  that  fJ  f  •        ''''"'^  '^^^*- 

charge  of  electricity  niust  be  hs  ,  :  '  ''  '"T'^  "  ^^ -^ 
-th  the  earth  through  a  conducti  g  ;  '  ^ta  o  "s  """f"'^ 
best  insulating  substances  are  clr,  a/.,  .^^2^  "" 
giass  (free  from  lead    p  n     n^  V      .  ^'^^'  «'«e//ac,  resins, 

b.''tterv  is  the  source  of  electrioitv  th!       ,  °  "  ^'''™"'° 

wood,  for  mBtaooe      wh  r f       ^'       '  ""''»'""«» -sueh  as  dry 

Jatter  case  «;  „ot  s7r™     ,  T-  T'T"^'  •*"""  '"»"'"'»-  »  «•" 
injures  the  iusrio,  Xdios!"        '"™"''      *"■'"'"'■«  ^'-''y 


ELECTRICAL  POTENTIAL. 


267 


or  example,  a 
ill-  a  pith-ball, 
st  side.  Two 
tlie  pith-ball, 
the  -f-e  of  the 
ling-wax  and 
8  less  iu  the 


electrified  seal- 
tnes  polarized, 
'ouch  the  she'll 
'  is  driven  to 
''}'  to  the  rod. 
the  rod;  test 
"icity.     (Is  it 
'parate  them, 
lectriflcation. 
^Mon  and  yic 
he  shells;  it 

ctric  charge 
t  is  evident 
I,  otherwise 
hich  do  not 
-ailed  wow- 
permanent 
connection 
>me  of  the 
"c,  resins, 
silks,  and 
state,  the 
I  galvanic 
uch  .as  dr" 
tors  in  the 
re  greatly 


§  215.  Electrification  confined  to  the  external  surface. 
—  Experiment  1.  Place  a  tin  fruit-can  on  a  clean,  dry,  -lass  tunil)lfr 
(Fig  IHO).  Fasten  a  circular  disk,  a,  of  tin,  l.V""  iu  diameter,  to  one  oml 
of  a  rod  of  scalinjj:-wax.  Charge  the  can  heavily  with  el.;ctricitv  from 
anelectrical  machine  (s.-c  §217).  Through  an  orifice,  c,  in  tl'ie  can 
introduce  the  disk,  and  touch  the  interior  surface  of  the 
can.  Withdraw  the  disk  and  present  it  to  an  electroscoi)e.  ^'^-  ^*'*- 
Is  the  disk  electrincd?  Now  touch  the  exterior  surfai-e  of 
the  can  with  the  disk,  and  i)resent  it  to  the  electroscope. 
Is  the  disk  electrified  tills  time? 


Experiment  2.  Attach  to  the  can  a  gold-foil,  or  double 
pith-ball  electroscope,  and  put  into  the  can  a  few  feet  of 
metal  chain.  Fasten  the  outer  end  to  a  rod  of  glass,  or 
some  other  insulator,  and  charge  the  can  till  the  leaves  of  the  electro- 
scope diverge  widely.  Then  draw  up  the  chain  by  the  glass  rod-  the 
leaves  come  together  somewhat.  What  does  this  indicate?  Drop  the 
Cham  mto  the  can;  the  leaves  separate  again,  showing  that  the  charge 
had  not  been  lost. 

These  experiments  show  (1)  that  no  electricity  can  be  found 
inside  of  a  hollow-charged  body  ;  or,  roughly  stated,  electricity 
at  rest  resides  on  the  exterior  surfaces  of  bodies;  (2)  that 
token  the  exterior  surface  of  an  electrified  body  is  incr  ..fd  with- 
out increasing  its  mass  or  the  charge,  the  amount  of  elect  icity  at 
any  point  is  diminished. 

§   216.    Electrical  potential.  —  We  have  seen  that  the 
passage  of  electricity  from  point  to  point  sometimes  causes  a 
spark ;  so,  conversely,  the  spark  indicates  the  passage  of  elec- 
tricity.    The  passage  of  a  current  from  one  shell  to  the  other 
(Fig.  179)  might  be  proved,  and  its  direction  determined,  by 
connecting  the  sliells  by  wires  joined  to  a  suitable  galvanome- 
ter.    The  current  would  flow  from  A  charged  with  +e,  to  B 
charged  with  -e,  thus  showing  that  A  had  a  higher  potential 
than  B.     A  body  charged  with  -\-e  is  understood  to  be  one  that 
has  a  higher  potential   than   that  of   the   earth,  and  a  body 
charged  with  -e  is  one  that  has  a  lower  potential  than  that 
of  the  earth,  the  potential  of  the  earth  being  regarded  for  con- 
venience as  zero. 


;i 


II 


ifi! 


268 


II  If: 

mi 


ELECTRrciTV    AXD   MAONETfSNf. 


"W"ith  a  very  sensitive  oleotroscono  ,>  «       u     , 
wires  connected  with   the  nhtes  T         '^"  """'  "'"'  ^'^'^ 

^'i«-erent  potentials  when    h^^   L    is^:t"""  '"^"^••'^'  ^^  '^^ 
ence  of  potential  is  so  small  T  '"'     ^"*  ^^e  difTer- 

<'"eed  by  friction,  that  a  U  o,  f  ^  ""'  ''"  ^^'"^^^^^^  P'^o- 
a^Parlconlyabo.:;::,:;:^;!^^^^^^^ 

Potentili,  l;!    t\t:7'"'^"""^  "-'^'^  ^'-*-''*y  o.  hi.h 
«on  coil    or    I^ch"^™r"""'^^^^-''^'- 
-achinedependin^eithero^:^ci""'""""^■'   "^"   ^'-^---I 
charge  of  electricity.     Brief  de  1,    ,'   ''  ""  '''  "-luction-of  a 

--  bo  given,  followed  b7a  ^e^of  ^  ''-"^  '^"  ™^^^"^^^  -'" 
performed  with  them.  experiments  that  may  be 

Fig.  181. 


made  of  two  cushions  of  leatTr  1^  \  ^  ''  P'''^'^  ^'  ^  ^"^ber  D 
•atin,^  supports  E,  p'g  a.Kl  h  ^ T'  '""'  ""  ^'"'^'^'^"^'  ^«»r  Insu 
c'>ain  K,  used  to  congee;  ettr.      1      '"'"''^""»  ^'"^^  ^'  «"^J  a  brass 

side  of  the  plate;  their  pointed  teeth  sr?,        1     ''°"'''"'  ""«  ^^  either 
ft pith-baU  electroscope  '"'^  ^'« *"^°«^  t«'-^ard  the  plate.   Mis 


«vii  tliat  the 
ttery  are  nt 
'  the  difTer- 
'ercnce  pro- 
serios  give 


IS,  ETC. 

ty  oi  'iigh 

an  iiiduc- 

eloctrical 

ction'of  a 

Aincs  will 

It  may  be 


^ 
^ 


r  prime 
bber  D, 
ur  insu- 
a  brass 
I  exten- 
1  either 
s.  Mis 


KLECTUOPHOltUS.  269 

When  the  plate  is  turned  in  the  direction  indicated  by  the 
arrow,  i    passes  between  the  rubbers,  and  the  friction  .venerates 

of  the  p  ate  then  passn.g  through  the  silk  bag  comes  opposite 
the  comb  when  .t  polarizes  the  prime  conductor,  attract!  - 
and  rq,elhng  +..  But  the  -e  escapes  from  the  points  of  the 
comb  (see  §  22G)  to  the  plate  and  neutralizes  the  +e  of  the  plate 
and  thereby  leaves  the  conductor  charged  with  +e  U  both  con; 
ductors  are  msulated  at  the  same  time,  the  mutual  attraction  of 
the  two  kmds  of  electricity  would  prevent  their  becoming  heavily 
Fig.  182.  charged,   so  one  of  the  con- 

ductors is  always  connected  to 
earth  by  a  chain.  If  +e  if, 
wanted,  A  is  insulated  ;  if  -e 
is  wanted,  B  is  insulated. 

§  219.    Electrophorus.  -» 
Experiment.    On  a  circular  dis^ 
of  shcot-iron  or  tiu  2G™  in  dianic- 
ti'r  ccineut  a  circular  dislj  of  vul- 
canite 22c'n  in  diameter.    To  the 
center  of  another  circu- 
lar disk  of  tin  18<;"'  in 
diameter  (Fig.  182)  ap- 
ply with  heat  one  end  of 
a  stick  of  sealing-wax 
for  a  handle.    Strike  the 
surface  of  the  vulcanite 
a  few  times  with  a  cat's 
fur  or  a  fox-ull;  it  will 
become  electrified  with 
-c.    Then  place  the  tin 
disk  ou  the  vulcanite; 
-e  of  the  vulcanite  will 
poi.xrize  the  disk,  indue- 

~,  WIU  eacpc  though  your  body  l„  the  c-arll..  tat  tho  IT^mvmX 


Fig.  183. 


i 


:B, 


I 


270 


BLECTRICITV  AND  MAGNETISM. 


on  the  disk,  bound  bv  the —^  r.r  ti.        i 

linger  and  ral.se  the  dii  ,n  it  LZn^Tu'  ''"'"^^'  ''"^"^'^  ^''^ 
influence  of  the  -.  „„  the  ,  t  H.  T  "  ''''''''''''  ''"^'^  *'•« 
and  if  a  k„„ekle  .,f  .,„.  of V       l!  2"  /^?  +'  "'  *'"'  ^"'^•^  ''^  ""^v  free, 

bright  spark  wil,  ,k.ss  fn  n  t^ vom/f  "'-/''V' "'"'"^'''^  "-''  '^  « 
charged.  ^  *  ^°"'  ^"^"'l'  an^  it  will  become  dls- 

n  Jl;:;^^^  S: :-uS:Sn1;^ -ll^^^^  "^--  —  a  .reat 
A  U,v.len  Jar  (page  ..0)  .na^  e^u    h  U  ''''  "'"'  "'^  '"'•• 

'""intcs.     (Is  the  disk  charged  by  contl     f  '  /'"•"^'•''tus  in  a  few 

the  proofs?)  °        ^  conduction  or  induction?    What  are 

§   220.    Continuous    electrophorus        \'n..; 
have  been  aaoi>to(l  for  clevoloni„.r  .k^.?,     7  ^  ''''^'''    '"^^^''^^^^ 
the  olectrophonts,  unci    Zro  ^^^^'"^•'t^' -"^"-ously  from 


Pig.  184. 


the  electrophorus,  und   more 

••ai)idly  and  with  less  manipu- 

hition  thiin  can  be  done  with 

tlie  apparatus  above  described 

I'^igurc   184,   from   which   the 

supporting  parts  are  omitted 
for  the  sake  of  simplicity,  will 
serve  to  illustrate  the  general 
principle  of  such  machines. 

A  is  a  vulcanite  or  glass  vj         -<tA  ^ 

wheel,  which  can  be  rotated  bv  means  of  o         . 
CC.     About  2-"  back  of  \  i  •         i  '^'''''"'  ^^  ^^^'^'1« 

as  an  inducer,  or  tL  sal  nurnn'    "";?'  "'^'^ '''  ^^"^'^  ^-ves 
electrophortts      O     os^  n      ^^^  T  '''  ""^'^"^'^  ^'^^^  «^  "^e 

^:--'Hiscon^r:iS:b:o:r^^^ir^ 

cited  on  D  with  a  cat-skin      Ti,       1  ^^  ~^  ^"^  *^-^- 

J^.      Ihen,  smce   electricity  escatDcs   ronrliil  f 

port,: J;  th!  „;?:!""  ^'"^'"s ,"  ""--"''-'«'■.  o.i/th: 


illy,  remove  the 
novetl  from  the 
lisk  is  now  free, 
oii^'Iit  near  It,  a 
ill  beconio  Uis- 

mauncr  a  great 
e  with  tlie  fur. 
iratiis  ill  a  few 
on?     What  are 


)us    methods 
miouslj  from 


I  of  wheels 
''hieh  serves 
iisk  of  the 
tallic  comb 
— e  be  ex- 
system  NIJ 
ven   to  its 
'  the  comb 
Joints,  the 
Its  by  the 
only   that 
|-«  that  is 
being  de- 
rotate  the 


TOEPLKU-HOLTZ   MACHINE.  O71 

disk  A      When  it  has  accomplished  half  a  revolution  tint  nor 
fon  o     :t  which   is  charged   with  +.  eo.nes  op  "  te  l      ; 
comb  H,  which  is  also  connected  with  a  conduct^   P      tC  1 
<lMctor  B'  P  becomes  polarized.     Its  _.  nassos  off  fL 
Loints  of  B  to  the  disk  A,  and  discharges  T!^  ^t       di  ^ 
wlue  the  conductor  VIV  is  left  char^.d  with  free  4^        jfl 
ovdent  that  a  constant  rotation  of  A  would  c'     so  it  tt  bo 

conducto.  B  N  is  constantly  receiving  a  change  of      n  in  nr. 
q.ience  of  the  loss  of  its  -Ce  •  and  for  •   In.  ~  '" 

dupfor  n>  i»  •  .  ^   '  ^  '^  similar  reason  the  con- 

«l<«ctor  B'  P  ,s  constantly  receiving  a  charge  of  +e      Wit    ' 
ra,Hd  rota.0.1  of  the  disk  the  two  condncto^  will  tso  l^; 
.  K  1"^^''  y  electrided,  the  one  with  -e  and  the  other  wit    + 

incessant  flon  of  sparks  will  p,iss  between  them,  even  when  th. 
extremities,  P  and  N,  are  several  i.iehes  apart.  " 

§  221     The  Toepler-Holtz  Maohii.       Fig.  185^  is  inntho. 

--  o.  .e  o.  „::;o„  i:,r.  "Tir  ::ri:r 

imsscs  a  Bpinc  e  to  wliicli  is  fiv,.,l    l.„  „     •       ,  ''^'^ 

a  revolving  .lass  ilteO  .'.^       ,',"''''"''"« •■'«'''^''""'. 

plate     0„  the  h.„       r  "'"""'■''' """'  ""^  «""ionary 

with .  a,„,  *, :;  ;,„  o\;  tt ; r'o"™;;,,!  "■":  k\  """""•'"" 
Lrri^^::r™"'"'''-^^^^^ 

rass  wire.     Bs  turning  these  screws  the  brushes  may  be  -u} 
justed  so  as  to  anniniph   o~  »  ,  •  '* 

•ovolviu^  nhto      'P  ?p       "'■  "'   ""'^''  ^"  ^'^«''-^^»   to  the 

eae.0^/:::..::— '-r;::;:-:--^ 


m 


ifii 


272 


KLECTRICITY  AND   AfAGNETISRf. 


f'-ont  of  O  and  opposite  tl,e  strips  of  tiu  foil  d  and  a      Tn  .. 

a  with  eadi  other  by  a  conductor  passing  uuder  the 

Fig.  185. 


'^'^'>^^TrafntSi:so*AS^^^^;^; 


TOEPLER-HOLTZ  MACHINE. 


273 


Vw^ 


ofy  y  and  c  c'.  By  means  of  the  wheel  W,  provided  with  a 
belt  passing  round  the  spindle,  the  plate  O  may  be  rapidly  re- 
volved. '' 

The  action  of  this  machine  is  in  the  main  the  same  as  that  of 
Ihe  Continuous  Elkctkophouus  (§  220).     It  will  be  observed 
that  It  IS  provided  with  mo  inducers,  d  and  d* .     The  L-sli'iped 
arms  y  and  y'  enable  the  revolving  plate  O  (by  what  means?) 
to  increase  the  charges  on  the  inducers  d  and  d\  so  th.t,  though 
these  charges  may  be  small  at  first,  they  rapidly  increase  to°a 
maximum  as  the  machine  '     vorked.    If  tlie  brushes  y  ,/  and  cc/ 
are  adjusted  so  as  just  to  couch  the  metallic  buttons  on  O    the 
infinitesimal  difference  of  potential  always  existin-r  between  d 
and  d'  ,s  enough,  when  the  atmosphere   is  in  a  favorable  con- 
dition,   to  start  the  machine.     When  the  condition  of  the  -it- 
mosphere   is  very  favorable,  the  machine    works  equally  well 
with  the  brushes  not  touching  the  buttons.     The  two  Leyden 
jars  act  as  condensers,  causing  a  greater  quantity  of  electricity 
to   accunmlate  before  the   difference  of  potential  between  the 
two  electrodes  is  sufncient  to  cause  a  spark  to  pass  between 
them      Ihe  rod  c  C  has  a  ten.lency  to  prevent  a  dischar<xe  tak-  ' 
ing  place  across  the  face  of  the  plate  O.     This  discharge  may 
be  observed  by  working  the  machine  in  the  dark  witii  the  rod 
cc'  removed.     This  rod  also  makes  it  easier  to  stnrt  the  action 
of  the  machine  without  first  charging  d  or  d'  from  some  external 
source. 

If  the  atmosphere  is  warm  and  very  dry,  and  the  machine  in 
good  order,  sparks  may  be  obtained  of  a  length  equal  to  five- 
sixths  of  the  radius  of  the  reviving  plate.  ^  The  inducers  or 
armatures,  as  they  are  generally  called,  must  be  very  carefJlly 
insulated  from  the  air.  For  this  pu.pose  it  is  necessary  from 
time  to  tune,  to  renew  the  coating  of  shellac-varnish  at  certain 
points,  particularly  at  the  edge  of  tlie  reyolviu-  plate  By 
working  the  machine  in  the  ,lark,  any  leaks  from  the  armatures 
may  be  easily  seen. 


m 


iMii 


From  what  you  know  about  electrical  attraction  and 


repul- 


274 


ELECTRICITY  AND   MAGNETISM. 


IH' 


n 


,  t 


It 


.Ion  can  you  see  .any  reason  why  this  machine  shonid  be  harder 
to  tmn  when  ,t  ,s  working  than  when  it  is  not?  That  yon  may 
be  able  to  answer  ti.is  question,  e..ann„e  very  careful  y  any  at 

p™ eZ,  that'""":;"""  '"'"■^^" '"'  »''«'™»^  °" «-  -°'v4 

plate  and  that  on  o(her  parts  of  the  machine. 

called  a  cuneHl-irmker,  by  means  of  which  the  induced  cur 
l-e'nt  between  the  outercoatings  .  an.l  ,  of  the  two  Cden   as 

out  and    he  ends  jomed  to  two  sliding  electrodes,  which  may  be 
l>l...'ed  at  any  distance  apart.     If  the  electrodes  of  the  machine 

aTa,?:::  trr "°r  "^'"^  cnr..„t.brea.er  are  notZ 
apa.t,  „hen  the  maclune  is  worked  sparks  will  pass  between 

bleaker      It  the  electrodes  of  (he  eurrent-breake.  are  held  in 

he  hands  and  the  m.aehine  is  worked  with  its  own  electrode,  sen" 

aated     a   senes  of  shocks  will    be  felt  whose  inteusi  rwUl 

apa  t  Wthh,s  attachment  the  Holtz  machine  may  often  be 
made  to  take  the  place  of  an  induction  coil. 

.ri!,f^^'  I .°°°'»™«'"--  -  A  very  in.portant  adjunct  to  an  elec- 
tr  cal  „,achn,c  ,s  a  coMlens..  of  some  kind,  by  means  of  whte  ■ 
a  large  quantity  can  be  collected  on  a  small  surface 

piac?,r=\„:i::s"r:i:r"^'r;;;sri«^ 

triH,!'iri''"'n  "r',  ""^  ""'  ''"""^^  ••'°  ™"»"»1  q'-^'-'ity  of  elce- 

IS  snnple      The  hand  of  the  first  |.erson,  charged  with  +c.  .a,-,, 

inV     "tthl""?"  "'%«'"^'  """"  "■'  ^«^""<'  l-"-"- a,  ,:^. 
mg  -c  to  the  surface  of  the  gl.ass  with  which  his  baud  is  in 


LEYDEN  JAR. 


275 


contact,  and  repelling  +e  to  the  earth.  Thus,  thrcgh  their 
mutual  attraction,  the  two  kinds  of  electricity  become  as  it 
vyere,  heaped  up  opposite  each  other,  and  yet  are  prevoiited,  by 
the  insulating  glass,  from  uniting. 

§223.  Leyden  jar. -The  most  convenient  form  of  con- 
Fig.  186.  *^enser  is  the  Leyden  jar.  Coat  a  green  glass  quart 
fruit-jar  (Fig.  186),  within  and  without,  for  about 
two-thirds  its  hight,  with  tin  foil,  using  flour  paste. 
Close  the  mouth  with  a  cork  saturated  with  hot 
parafflne.  Through  the  cork  pass  a  stout  brass  wire 
till  It  touches  the  inner  foil.  Cast  a  lead  bullet  a  on 
the  exposed  end  of  the  wire.  Clean,  warm,  and  var- 
nish the  exposed  glass  surftico  of  the  jar,  and  when  thorouakly 
clri/  it  IS  ready  for  use.  ^ 

The  jar  may  be  charged  by  connecting  one  of  its  coatings 
w.tii  the  +conductor,  and  the  other  with  the  -conductor  of  an 
electr.cal  machine,  or  by  connecting  one  of  the  coatings  with 
Fig.  1.7.  one  of  the  conductors,  and  the  other  with 

the  earth.  Or  it  may  be  charged  by  con- 
necting the  outside  coating  with  one  of  the 
poles  of  the  secondary  coil  of  an  induction 
coil,  and  bringing  the  other  pole  near  to  the 
ball  leading  from  the  inner  coating.  To 
„  .„  ,,     ,      ,  discharge  the  jar,  connect  the  outer  coating 

with  the  knob  of  the  jar.  To  avoid  a  shock  in  so  doing,  prepare 
a  discharger  as  follows:  Tlirough  the  cork  of  a  bottle  (e.r.,  a 
soda-water  bottle,  Figure  187)  pass  a  stout  brass  semiclrc4iar 
wne.  Cast  f,n  each  of  its  ends  a  lead  bullet.  Use  the  bottle 
as  an  insulating  handle. 

The  effects  are  greater  in  proportion  to  the  number  and  size 

rFi!"  ^Z  r"  ""T'f  ^""»^^^'-^-  Let  any  number  of  jars 
(1  ig.  188)  be  placed  on  a  sheet  of  tin  foil,  by  which  their 
outer  coatings  are  connected.  Connect  also  their  inner  coat- 
ings with  one  another  by  a  wire  ru.uiing  around  their  projectino- 


m 


iLiil 


ill 


276 


ELECTRICITY  AND   MAGNETISM. 


into  one  latgelln'  ^'ZTclll^^'^'T  P''^«*'«''^"y  converted 

be  fused,  and  eten  vol  t  li.rd  V?  "^'  ^^''^'^  ^^'^  «  ^^^ 

through  it,   cards  a.^'ln  f^  1^ '^  7^  "^  ^^  ^^^^^ 
gas  or  ether  ignited.  °  ■'^        Pwlorated,  and 


Pig-  188. 


5  224.  Bleotrioity  not  in  the  coatings  -If  n,„  , 
sons  m  the  experiment  (S  -I-i-n  k„»t         °*^-     "  '""  two  per- 
the  glass  plate    after    hit  ,       '',°"' "'"°™  "">'■•  hamls  from 

replaee  their  hands  o^,  tS  a  ,  Z  ""  '""^''-  """  '^  '"^^ 
they  reeeivo  a  shoek.  TO  show,  ^.i^  """""""^  '■"°<'«' 
their  hodies,  but  on  the  surfae  ^n,,  It  ThT  T  ""'  " 
r-eyden  jar  serve  the  purpose  of  oonlf        .  """'"«'  "'  " 

on  the  glass  at  the  tfme'Tf  „ha "  ntt^  f  T"' .**-''^- 
«-om  al,  parts  oHts  eleetri«  sS^  t  '^JtT.ZZ^ 

QUESTIONS. 
1.    ^°J"«»'ated  jar  ca»uot  receive  a  great  charjre     Whv? 


ATTRACTIONS  AND  REPULSIONS. 


277 


Fig.  189. 


«.  If  the  knob  of  i  second  jar  be  held  near  the  outer  coafJno.  ^f  a« 

ovulated  jar  sparks  will  pass  from  the  coating  to  t.  Lkn^  and  bo" 

jai  8  will  be  charged.     Suppose  that  the  ,nner  ctatlng  of  the  flr  t  jar  1« 

«  5^;  Attractions  and  repulsions. -Experiment  i.  Sup- 
P^rt  a  plate  of  window  glass  (Fig.  189)  about  S-n  from  a  tabic.    Rub  its 

upper  surface  with  a  silk  handkerchief 

and  place  plth-balls,  or  bits  of  tissue  paper,' 

on  the  table  beneath  the  glass.     They  will 

dance  up  and  down  between  the  plate  and 

_,        .  _  table  in  a  lively  manner.     (Explain.) 

Experiment  2.  Place  a  handl\il  of  bits  of  tissue  paper  on  a  tin  disk 

■  upported  by  a  prime  conductor  of  an  electrical  nmd.lne.     The  papers 

t, come  excited,  are  repeUed  into  the  air.  and  fall  on  all  sides.  gMng 

tt,  e  appearance  of  a  miniature  snow-storm  ^ 

a  .  Sw"'°f  frl  ^?^^  °"'  '"^  °^  *  discharger  to  the  conductor  of 
a  V  .achine,  and  the  other  end  to  the  inner  surface  of  a  glass  tumbler 
oithbar'  *f  interior  with  electricity,  and  then  place  It  overtme 

The  electric  whirl  consists  of  a  cap  of  metal  resting  upon  a 
pointed  wire,  which  serves  as  a  pivot.     The  cap  lias  pointed 
wires  branching  out  from  it,  like  tlie  spokes  of  a 
wheel,  and  bent  near  their  ends  at  right  angles, 
and  all  turned  in  the  same  direction,  as  shown  in 
Figure  190.    When  this  apparatus  is  placed  upon 
the  conductor  of  a   machine,  the    air  particles 
around  the  highly  electriiled  points  become  ex- 
cit«d,  and  are  repelled,  producing  a  current  of  air 
issuing  from  the  points.     Tlie  reaction   causes 
t^  wheel  to  revolve  in  the  opposite  direction,  as  indicated  by 
the  arrows  m  the  figure.     A  candle  flame  placed  near  the  point 
ot  a  rod  attached  to  a  conductor  will  be  extinguishod. 

§226.  Effect  of  points. -We  might  reasonably  expect 
that  a  current  of  excited  air-particles  issuing  fl-om  points  on 
m  excited  conductor  would  serve  to  carry  away  with  them  elec- 


Pig.  190. 


il 


;■•'■ 
liji' 


f' 


278 


ELECTRICITY  AND  MAGNETISM. 


will  pass  to  your  knuckle,  or.  at  most,  very  feeb  e  o^esin  l        ""T" 

seconds  after  the  operation  of  gener-  '  ^°'^  '"  ^  '^''^ 

ating  electricity  ceases,  the  conductor 

will  be  found  completely  discharged, 

although  it  Is  thoroughly  insulated.  It 

Is  apparent  that  the  electricity  escaped 

from  the  points. 


Fig.  191. 


r*,^"-^ '^""^v, 


We  conclude,  therefore,  that  the 
effect  of  points  on  an  elect nfied  in- 
sulated body  is  greatly  to  facilitate 
the  discharge  of  its  electncity. 

§  227.  Luminous  effects.  — 
Figure  191  represents  a  glass  shade 
having  circular  bits  of  tinfoil  pasted 
spirally  around  it,  from  top  to  bot- 
tom, and  about  1™™  apart.  If  the 
poles  of  an  induction  coil,  or  the  ^up 

conductors  of  an  electrical  machine,  are  connected,  one  with 
each  extremity  of  this  spiral  line,  an  intermittent  li  le  of  l" 
will  be  produced  in  the  path  of  the  current  by  the  sparkrwhT  h 
appear  at  the  intervals  between  the  bits  of  foiL    All  ex^ei  inT 
mustraung  luminous  effects  should  be  performed  in  a  dLCom 
Beautiful  luminous  effects  may  be  produced  with  apparatus 
arranged  as  follows  :  Apply  to  one  surface  of  a  mica  dT  F i^ 
192),  about    0  X  10-,  a  sheet  of  silver  leaf  or  tin  foil,  8  x  5- 

within  1      of  the  foil,  and  as  far  apart  as  the  power  of  the 
macl-o  w.  1  admit.    Sparks  will  leap  from  the  poles  to  the  foi^ 
and  travel  m  tortuous  branching  lines  between  the  pole«.  ' 


LUMINOUS  EFPECtS. 


^79 


tmrge  it.    Do 


peratiou,  hold 
irks  will  pass 
points  on  the 
■her  no  sparks 
and  in  a  fe\Y 


,  one  with 
le  of  light 
arks  wJiich 
fperinieiits 
lark  room, 
apparatus 
disk  (Fig. 
i,  8  X  5«''. 
machine, 
er  of  the 
o  the  foil, 
es. 


If  the  air  is  partially  exhausted  from  the  glass  tube  used  in 
Illustrating  the  law  of  falling  bodies  (Fig.  87),  and  the 
poles  of  a  coil  or  machine  are  applied  to  the  opposite  extremi- 
ties  of  the  tube,  sparks  of  electricity  passing  through  the  rarefied 
air  spread  out  ia  sheets  of  bluish  white  light  resemblin-  the 
auroral  lights,  hence  this  tube  has  received  the  name  Awora 
tube. 

Fig.  192. 


If  a  circular  disk  is  divided  into  black  and  white  sectors,  as 
In  Figure  193,  and  rotated  very  rapidly  in  ordinary  daylight, 
the  colors  blend,  and  the  disk  appears  of  a  uniform  gray  color. 
Fi.;.  103.  But  if   the  disk   is   illuminated  in   a 

darkened  room  by  tlie  electric  spark, 
each  sector  appears  separate,  and  the 
disk  appears  to  be  at  rest.  A  rail- 
road train  in  rapid  motion,  and  even 
its  wheels,  appear  to  be  at  rest  when 
illuminated  on  a  dark  night  by  a  flash 
of  lightning.  This  shows  that  the 
duration  of  an  electric  spark  must  be 
^'''i'3'  ^I'ief,  inasmuch  as  it  fails  to 
illuminate  these  objects  in  two  successive  positions. 

The  remarkable  beauty  and  brilliancy  of  the  discharge  is 
perhaps  best  exhibited  by  me.ins  of  the  well  known  Geisder's 
tubes.  These  tubes  contain  highly  rarefied  vapors  and  gases  of 
various  kinds.  Platinum  wires  arc  sealed  into  the  glass  at  each 
end  to  conduct  the  eliH-tria  current  through  the  glass.  The 
light,  instead  of  appearing,  as  ii  the  Aurora  tube,  like  a  stream 


01 


If 


m 


ttECTBtOITV  AK,,  MAONCTtHM. 


I^«.  194. 


"*"'  ^--«  "-'  When  „i.  X;„  :Sttr"''  ""'^'' 

dmtely  beneatli  the  cloud  L,  "''J"""*  *''"«'™  tame- 

opposite  kind  of  eiecSy  Tll  7"  """'"''™'^  -""  '"» 
spond  to  the  coatings,  aid  the  ■?,  "  "'"^  ""^  ""«''  ""^ 
l""go  Leyden  Jar.    The  Ztch  ■"'",'*  "'''  '^  *'"=  S'-''^'  of  a 

^  "old  one  another  prirn  r^v         ""'  """  """  ""  "■«<"o"d 

".e  charges  aeen™„',a^  thed;;";"""  ""-""''°"'  ■"""•  - 
overcome  the  -istance^f  tht  ntt  .itZ™  f  ™'  ™""'"'"  *" 
takes  place.  It  is  the  acenmnlation  oM  '  '  W'™.  "discharge 
elevated  objects,  sneh  as  bnildt  "''"''"«''  o'ectricity  on 
«ttraetio„  for  the'  oppo  itT  eWrS  Tl  "?'  ."'"'  "«-'  "" 
«.em  especially  ,iab,r,»  be  strueT;!;  ligtotaf      ""'  """"" 

§  229.   Lightning-rods  —  Ti     a    u 
of  least  resistance.     A  good  liXll  l^  ^"'''  '^'""^  ^he  line 

ful  .eans  of  co.n,„nicrti  n  ttZ'Z.T  ^^^^^  ^  ^^-- 
leaJs  the  electricity  of  the  ZT  ^  ''"*'  ""^'  '^  ^^^"d :  it 
and  allocs  H  to  -r  1  ^''"^'>'  "P   townnl  tho   clnn.^ 

^  ^""'"^  "'^^  ^^«  «H-ite  wlthout'disttbtef: 


GENERAL   OB8EUVATIONS. 


281 

thereby  so  far  dischargmir  the  clonrl  ««  f 

stroke;  or,  if  the  tension  ts  too  t       to  ^^^^  ?  ''""'"-^ 

of,  the  flash  strikes  downwardtlnd  I  led  h  ""^ ''""^^"^^ 
earth  by  the  conductor       in     ?         /  harmlessly  to  the 

ducting  material,  so  lar^  thaTt  ^'J""^^*^  ^^  ^^^^^  ^«»- 

fnnn  loose  join  s      Tiflo  ,    u''^'  ^'  ""'^'''"^^  ^^^'^  f''«« 

t'-  ^s  aiwaj-s  tist"::dt:\rp ;  r^^^^^^^    .^"  r 

several  sharp  points.  terramate  in 

when  we  coosider  that  a  n,rf  „f  .,  ^7  """=  •"""='■.>•  ■?  evident 
the  ah-,  for  in«t  ,ee  ta T  T  .  ""•°""  '^  "'«>''  ""•"■'Sl> 
the  p,aL  and'rr  "  'l^ZZT:'  t"!"l "?  ''""°^" 
yield  a  strong  cnrrent  is,  ordTnarUy  ofl  1 1  T  '' ■'""  """"'" 
tlie  amount  of  „ork  th^t  T    ,    ^;  "■"'""'  "'»«m"cli  as 

"ona,  to  thes,r„rtLrn;ro:  Ltr„^^'-rf--- 
rs:irt::;:rrra^""^^ 

tio.  a  certain  eiairelXtiXrrnr"^"^  "  '"™''- 

.-ThiaTirr^^^^^^^^ 

tainedthat  the  duration  of  the  snark  Tin      .  T  "*""- 

the  .niiiionth  part  of  a  seeon^,  and   h'voeLoT;  ''^?  T 
discharge  from  a  Lovrlon  ^n.  f-         ,  »«iocicy  ot  the  electric 

is  280,0°00  mires  i,!^!''™?:!         "^    "  ''"'^'  """"  <=°PP-  -■■« 

The  phenomena  of  elecMcihi  /«   r,  .*  *•    , 

magnetic,  pkysiolo,ic„i,  cl^e^ica't^ZdJl^t    '""'•'"'-. 
prodwid  by  electricit,,  ,•«  ,h.  \,         mtsclumml  effects  can  be 

former  Je    TleeZ  Z    !    .'""'"'""  '""^  '""i'-     '"   «« 
«r?«,Stt,  Jy/'*  '"'   '"'■^'^''-   •»   '*«   '««»'■   .■<  travels 


fit' 


'^.'1 


till  I 


282 


ELECTRICITY  AND   MAGNETISM. 


M 


Much  18  known  of  electricity,  its  nature,  its  laws,  and  its 
capacity  for  worii ;  miicli  remains  to  be  learned.    The  question. 
What  is  electricity?  is  so  far  unanswered.     But  we  may  r^asoil 
as  follows  concerning  it,  and  the  conclusion  answers  all  practi- 
cal purposes.     For  example,  the  energy  of  the  chemical  combi- 
nation  of  coal  and  oxygen  in  the  furnace  is  transformed  mto 
heat,  heat  works  an  engine,  the  engine  rotates  a  coil  of  wire  in  a 
magnetic  field,  the  motion  of  this  coil  in  the  vicinity  of  a  magnet 
induces  currents  of  electricity  in  the  wire,  these  currents  pro- 
duce  an  arc,  and  thereby  heat  and  light.     So  the  energy  of  the 
coal  is  transformed  into  heat  and  light,  through  the  intermediate 
agency  of  electricity.    Hence,  it  is  certain  that  this  intermediate 
agency,  this  so-called  electricity,  whatever  it  is,  may  receive  and 
impart  energy. 

§  231.   Transformation  of  energy.  -  We  have  found  that 
every  contnvance  for  the  development  of  electric  enevgy  is  simply 
a  machine  for  the  transformation  of  some  other  form  of  encrnn 
into  electric  energy.     In  the  voltaic  battery  the  chemical  poten- 
tial  energy  of  the  combustibles  is  transformed  into  the  kinetic 
energy  of  the  electric  current.    With  the  magneto  and  frictional 
machines,  mechanical  energy  is  transformed  into  electric  enercry 
In  the  thermopile,  heat  is  changed  directly  into  electric  energy 
By  means  of  an  induction  coil,  the  fnll  of   a  large  quantity  of 
electrui'y   through   a   small    difference   of   potential    raises   a 
small  quantity  through  a  great  difference  of  potential       The 
kinetic  or  current  form   of    electricity   may.  under    suitable 
conditions,  be  converted  into  the  potential  or  static  state,  and 
vice  versa.     Not  only  are  these  various  forms  of  energy  trans- 
formable  into  electric  energy,  but  electric  energy  may  be'^changed 
into  any  one  of  these.    Thus  electric  energy  may  be  transformed 
uito  heat,  magnetism,  light,    chemical  action,  and  mechanical 
motion.     These  forms  of  energy  are  all  interchangeable  :  as  in 
fact,  all  known  forms  of  energy  are  mutually  convertible. 


TRANSFORMATION   OF  ENERGY. 


283 


Lws,  and  its 
lie  question, 
may  reason 
's  all  practi- 
nical  conibi- 
forined  into 
of  wire  in  a 
of  a  magnet 
irrents  pro- 
ergy  of  the 
ntcrmediate 
iitermediate 
receive  and 


found  that 
VJ  »s  simjily 
I  of  encn/y 
lical  poton- 
the  kinetio 
d  friction  al 
;ric  energy. 
rie  energy, 
[uantity  of 
1   raises   a 
-ial.      The 
r    suitable 

state,  and 
;rgy  trans- 
)e  changed 
ansformed 
nechanical 
ble ;  as  in 
ble. 


The  woik  done  by  a  pound  of  matter  in  falling  through  a 
distance  of  one  foot  at  the  surface  of  the  earth  is  called  a  foot- 
l)ouu(I  (§  89).  It  has  been  determined  that  the  work  done  by 
one  coulomb  (§181)  of  electricity  in  falling  through  a  differ- 
ence  of  electrical  level  or  potential  of  oi.e  volt  (§182)  is  7373 
of  a  foot-pound.  Hence,  the  work  done  in  any  part  of  a  circuit 
in  a  second  may  be  calculated  when  we  know  the  stren-^th  of 
the  current  in  arapi^res  and  the  full  in  potential,  in  that  p'Lrt  of 
the  circuit,  in  volts. 

-   Example  1.     Find  the  work  ilone  in  one  second  in  an  arc  lamp  (8  23o) 
he  stn-ngth  of  the  current  i.olnj,.  10  ampere,  and  the  resistancx>  of   tl  e 
lamp  5  oliias. 

To  n.ahitain  a  current  of  lo  amperes  throujrh  a  resistance  of  5  oinns 
will  re(iuu-c  a  fall  of  potential  of  50  volts  (§  isi) 

Hence,  hi  this  case,  we  have  a  fall  of  lo"  coulombs  through  50  volts 
each  second.     Therefore,  the  work  done  per  seconil  is 
10  X  50  X    .7,373  foot-pounds 
368.C3     " 
Therefore,  the  work  done  per  minute  is 

3(J8.(i5  X  CO  =  22, Hi)  foot-pounds. 

Now,  one  horse-power  is  required  to  do  33,000  foot-pounds  of  work 
per  nnnute  (§<)0).  Therefore,  it  requires  about  two-thirds  of  one 
horse-power  to  do  the  work  done  in  this  lamp. 

Example  2.  What  horse-power  is  reciuired  to  maintain  a  current  of 
5  amperes  through  a  resistance  of  100  ohms? 

To  maintain  a  current  of  5  amperes  through  a  resistance  of  100 
ohms  will  re(iun-e  a  faU  of  potential  of  500  volts  (§  181) 

mZlts  "'  *'"'  '''''''  '''^  ^'^^^  ""  ^^'^  ""^  ^  coulombs  per  second  through 
Therefore,  the  work  done  per  second  is, 

5  X  500  X  .7373  foot-pounds 
1,843.25     "        " 
Therefore,  the  work  done  per  minute  is, 

1,843.25  X  GO  foot-pounds 


Therefore,  it  requir 


110.595     " 


'es 


110,595 


TiT;;;  =  3.35  hor.se- 


do,m 


power. 


1^1 


284 


ELBCTRICITV   AND   MAGNETISM. 
EXERCISES. 


2.    The  m...,ll,.  ..r  V^'  '  *"  ^''^'  ""'"  '"'-'^^u't- 


I 


It! 


XXXVr.     tlSEPITL    APPLICATIONS    OF   ELECTUICITY.        " 
§  232.  Medical  and  surgical  oDfirflfir.r,o      f^ 
.»  iuductiou  coil  have  ,ir.Jl^^lT\^°^-~''YT''  '""^ 

iunum  b«Ij.  and  ,„.„<1,k.  vi„l„  ,t    1  ^       t  f  J  T"^  °' ,«- 
rents  induced  Ijy  a  sin,>lc  volt-uc  ,,.      n         ',"''"""""«'•     tur. 
an  indncticn  co^l,  .na/p::,^':^     i' jr:!  v    Lr't"  1 
ta.o  current  l,us  a  sinnlar  effect  al  ti.e  iLt-."  ,    ,f       >  •       ' 
brcalcing  tl.e  oireui'  l,vl,vJ^■  l,„f  i     ,  ""'""§  •■""' 

impunity.     (Explain  ^     Tho  nl      •  ;         ,         ^^  ^  P"'"^'^  ^'^^ 

-».  ...u,  ;;.x,rs.;ri:*  ;';•:■*;:•  -■ 

uol  current  produces  .i  1,enui„bin.r  infl„e„  •  *'''" 

pain.     A  to-and-fm  n,„tion  „       e  e  ,  "ut'  i;  'T  '"^"'-""lity  t„ 
agitation  of  the  part  tln„u,-l,  „    ic      ,  "s  7  "  ■""''^"'"'' 

stimulating  cffccti  of  whicir  ar^   "i  .ij^  ^        ,'°""  ""' 

n"lr-..i^nnr^"'n-^'""-^^^^^^^^ 


ELECTRIC  IJQHT. 


285 


»les,  filled  with  a 

galvanic  current, 

10  battery,  stale 

suit. 

a  thermopile  j  j 

rned. 

u  electric  llyht. 


THICITY. 

Currents  from 
il  t'loetricity, 
issues  of  the 
:jtions.     Cur- 
mediation  of 
3US.      A  vol- 
making  and 
i  a  mild  ctw- 
th,  a  current 
I^erson  with 
duced  by  an 
tlian  at  the 
ir,h  one  pol( 

The  gra(' 
fusibility  to 
a  muscular 

tonic  and 
f  muscular 
crful  elee- 
'•  has   been 

sed  like  a 
advantage 


over  the  latter  in  that  it  sears  the  extremities  of  the  blood  vea- 
sols  and  t  o..by  prevents  hen.orrhage.  Enough  has  b".  Id 
to  show  that  a  medical  practitioner  who  canTtpply  the  laws  of 
e..tnc,ty  has  at  his  com.naud  a  powerful  therlp'utic  ag't 
b..  except  m  expc-rienced  hands  it  is  likely  to  prove  useless  W 
not  positively  dangerous.  ^  ^'  " 

S  233  Electric  light. -If  the  tei-minal.s  of  wires  from  a 
":::;;  ^^^';";r-^-^-'  ".aclnneor gmvanic  batterv  are  1  Tght 
ogether  and  then  separ.-.ted  1  or  2  n.illimoters,  the  cu,  rent    loJs 

not  cease  to  flow,  but   volatilizes   a   porti.m   of  the   tern  i,  Us 
he  vapor  formed  becomes  a  conductor  of  high  resist  nc^fd 

^annng  a    a  vei^  high   temperature    prodt^es  intens^^;  , 

pt  nty.  Ihe  heat  is  so  great  that  it  fuses  the  most  refractorA 
substa-ices,  mclu.ling  even  the  diamond.  Metal  terminals  quiokh 

that  the  electro-motive  force  is  no  longer  sufficient  for  the  in- 
creased^resistance,  and  the  lightis  extinguished.  Hence  pencils  of 
carbon  (prepared  from  i^c'i«^ns  or 

Fig.  195. 
^  B 


coke  deposited  in  the 
distillation  of  coal  in- 
side of  gas  i-etorts), 
which  are  less  fusible, 
are  used  for  1  terminals. 
For    simple    experi- 

Thm  rods  slide  ,n  brass  heads  A  and  B,  ,„pportod  h,  insu- 
IntlCaW.     "  ""  """""^  """""'  '"'  -^'-"'"'"'^ 

§  m  Voltaic  aro.-Tho  light  is  too  intense  to  admit  of 
examination  with  the  naked  eve ;  but  if  an  image  of  the  teli 


286 


ELECTEICiTY  AKD  MAGNETISM. 


Fig.  190. 


aals  is  thrown  oo  a  screen  bv  means  nf  ,  l„„.  •    . 

a  car,),    an  arch-shaned   hIm  '  °''  "  '""■'=°'°  '" 

•o   polo,   as   show,  Tf  f  ,0C    "r,"-  "V",""?   '""^   "* 
"-  -,„e  ot  the  .„,J:;,      \Jl':.    "'""    '-»»    ™--od 
h-,rl,f   I,  '"'="''    l""''""    "f    llle 

light,  however,  emanates  fron,  the  tips  of  the  two 
carbon  terminals,  whieh  are  heated  to  an     ,te„™ 
wmeness,  h„t  some  from  the  are.     'ne  ;por 
■otter  than  the  -pole,  as  is  shown  by  itstCin,^ 

the  +p„le  beeoraes  volatilized,  and  the  ligh,-<,ivin,. 
part,eles   are  transported    from  the  +po°,,.   To  "h^ 

t.,epoies.  wl::;^:re''^n;t2;l;"'::r™'''>■■•^--" 
-  w.  apa,^  i,.^  =r::^:;~:rr;;::;o: 

§  235.     Bleotrio  lamp.  —  The    -4-nnl„  „„  . 
twiee   as  fast  as  the  -note       At  +''"'"  .''"""''^  ""•■'J  »'>out 
conicaUhaped  cavity  is  ?„  Ld  thi      a,'"'    ,  »''  ""  ""'"""" 

latter  warty  protnberanees  ,^  'a         v  ^'in  eo"  """"  "'  "'° 
the  wearino-  awnv  r.f  fi  .  '  '"  consequence  of 

penciiX-omTL  ;::  f^"  "tl.e  let '"""  '"''''"'  "^  '«o 

li^ht  goes  ont.  Nnmioitifi  i' ;:  irz'f::  ,:r;  ■"° 

ing  a  nniform  distance  between  the  noles  ,  ,  """Ham- 
Such  an  arrangement  is  called  L,  I  "?  r""  "","■ 
carbons  are  ,„oved  bv  clock  w,„l    TT-^  ■  "°""''  "'" 

-asionally,    in  otlJs   ;!:':.  ;,r,T,"r  r"'""=  "" 
complished   autonratieally  by  the   a^r If '';,;:;,'.:;:.  ;:,-; 

vialf ali  n!t::;rna;:rJ' ^:/-r -'""''''  "'"- 

s.ae,  aand  b  (F,g.  19,),  separated  by  «  thin  insulating  septum! 


BLECTIIOTYPING. 


287 


I"  a  pin-hole  in 
ing   from   pole 

has  received 
M-tion  of  the 
ips  of  the  two 

to  an   intense 
The  -|-poIe  is 
y   its   glowing 
I'lie  carbon  of 
le  light -giving 
+pole    to  tlie 
k'apor  between 
iinoiiti  matter. 
cr,  as  may  l)e 
■tallic  poles,  a 
k  can  be  pro- 


■  awaj  about 
the  former  a 
point  of  the 
asequence  of 
^een  the  two 
to  span,  the 
or  mainlaln- 
Jen  devised, 
n  some,  the 
winding  np 
bons  is  ac- 
irrent  itself. 

-Hudle  "  ob- 

instead  of 

ced  side  by 

ng  septum, 


c,  of  kaolin.  The  current  passes  up  one  carbon,  across  the 
space  between  the  points,  and  down  the  other.  In  its  passage 
between  the  points  it  forms  the  luminous  arc.  The 
heat  of  the  arc  fuses  and  volatilizes  the  kaolin,  and 
it  wastes  slowly  away  like  the  wick  of  a  candle ; 
hence  its  name. 

The  electric  light  is  of  the  purest  white.  In  it  the 
most  delicate  colors  retain  their  noonday  purity  of 
tint,  while  a  gas  light  appears  of  a  sickly  yellow  hue 
in  comparison. 

§  237.   Blectrot3rping.  — This  book  is   printed 
from  electrotype  plates.    A  moulding-case  of  brass,  in  the  shape 
of  a  shallow  pan,  is  filled  to  the  depth  of  about  one  centimeter 
with  melted  wax.     A  few  pages  are  set  up  in  common  type,  and 
an  impression  or  mould  is  made  by  pressing  these  into  the  wax. 
The  type  are  then  distributed,  and  again  used  to  set  up  other 
pages.     Powdered  plumbago  is  applied  by  brushes  to  the  sur- 
face  of  the  wax  mould  to  render  it  a  conductor.     The  mould  is 
then  flowed  with  alcohol  to  prevent  adhesion  of  air-bubbles,  and 
afterwards  with  a  solution  of  copper  sulphate,  and  dusted  with 
iron  filings,  which  form  by  chemical  action  a  thin  film  of  copper 
on  the  plumbago  surface.     The'ease  is  then  suspended  in  a  bath 
of  copper  sulphate  dissolved  in  dilute  sulphuric  acid.  The  —pole 
(why  the  —pole?)  of  a  gnl  van  ic  battery  or  dynamo-electric  ma- 
chine is  applied  to  it ;  and  from  the  -f  pole  is  suspended  in  the 
bath  a  copper  plate  (why?)  opposite  and  near  to  the  wax  face. 
The  salt  of  copper  is  decomposed  by  the  electric  current,  and 
the  copper  is  deposited  on  the  surface  of  the  mould.     The  sul- 
phuric acid  appears  at  the  -fpole,  and,  combining  with  the 
copper  of  this  pole,  forms  new  molecules  of  copper  sulphate. 
When  the  copper  film  has  acquired  about  the  thickness  of  an 
ordinary  visiting  card,  it  is  removed  from  the  mould.    This  shell 
shows  distinctly  every  line  of  the  types  or  engraving.     It  is 
then  backed  with  melted  type-metal  to  give  firmness  to  the 


HI 


m 


288 


ELECTRICITY  AKD  MAGNETISM. 


-■"io,  with  the  iatte.,  It^^Z^t  Z  ""'""  ''  "  "'"°^"=''' 
ces»os  arc,  in  tl,o  main,  the  JZ       r      ''"'T""'"'-     Tl>«  Vo- 


Fig.  198. 


1,11 


m  . 


I 


battery,  and  then  a  Dhtp  ,.f(i,„ 

leposited  on  the  giv™  arti  t,  i""'    '""  "'"'''■•"  »"'  -  'o  be 

to  bo  deposited.     The  ^^1^    'T  °^  "  ^»"  »'  «h»  metal 

-a  for  gilding  and  .ui  ':  m1  rri,'";"  "^  ^'=-™"^ 

qUTe  to  be  eleetro-copnered  fir  f  i,!     i        "=  ''""'  """"b  re- 

of  .1.0  gold  or  silver.    Tre"™',  "f"^  '"  'o^-o  *«  adhesion 

completely  replaeed   the  vol  a  "Ta;';    '"r"  """"'""  ""»  """o^t 

•electio-plating  purposes  ""'■'  '°''  ^''=<=""typing  and 


THE  TELEGRAPH.  289 

§  239.    Electric  motors       le  ^  ,      -    , 

passed  through  the  ZuofTa!  T"'-"^  '^'^^""'^  '' 

so,,,e  exter,...,l  so,„ce,  the  armature  of  the   m.aeh"o        toIZ 

cngme.      A   djnamo   th„s   used   is   called   an   electric  motor 

s  earn  or  water  power,  and  the  two  dynamos  may  be  a  lon^ 
distance  apart,  so  long  as  the  cirouit  ionnecting  them  is  w  ll 
.nsnlate,!  uud  has  not  too  high  resistance.  Thus  a  p'wev  for 
example  a  waterfall,  may  be  used  to  perform  work  at  a  d  stae 
of  many  m.les,  while,  by  placing  several  small  dynamotsed 
arm  *"""  "'  '"'  large  dynamo  use'd  aTage  ' 
m  y  be  de Ter";:  '"''  '"'  -«^'"''"'»<'  ^  a-^  e.tent^hat 

™Lm:r:ppi,rith~-ra;ir-  - — 

"dually  it  Is  applied  only  to  electrical  methods  *     '     "' 

First,  ,t  should  be  nnderstood  that,  instead  of  two  lines  of 
w.re,  one  to  convey  the  electric  current  far  awav  froL  »T,    ! 
tery,  and  another  to  return  it  to  the  batterv Tth  T,    ! 
is  connected  with  a  large  metalli'o'  1^ ^  h        n'm^ ^ In  ° 
andf!    H '"'  1'"  '  ^"  "'  "'^^  f'^  *»'  l^ads  tT      cart' 

r^.t^h,r;,-tr-~r:;-n 
XX,i:'ro;t^;;ri-^^^ 

an-  of  the  ground  connections,  there  is  a Tav    g^f  LZS 


I 


290 


ELECTKICITY  AKJJ   MAGNKTISM. 


is  broken  at  B      Jot  thn  ^..      ,   ^^'     "  ""^^  '^e  seen  that  the  circuit 

key.  He  cToL  i^^^Z^^TZ^'  '°'"''  ""  "'^  '^^^^^  ^'  "'« 
wire  from  Boston  to  Ne  v  Yor^  It  t  I  '""'"*  *"^*"""^  «"«  t'"' 
lever  6,  and  presses  tlfe  point  'f  a  ty^'^n  fs?-  %'""^  '"^'"  *'^ 
drawn  over  a  rolI.T      The  nZvlL  '*"P  ''^  P'^P^''"  «  ^^^t  is 

Circuit  is  broken,  and  !^ZZ  r^sTd  fZ'Z  IT  t  '■^^'  "'^ 
spring  d.     Let  the  operator  press  udo     tt  i  ^    i^  ^^''  ''^  *  'P^"''^ 

long  enough  to  count  nn«  „  ,^,      *'"'  ''*'^'  **"^y  for  an  instant,  or 

tl.eWer''B:tTrrepres;e;Z^^^^  indentation  wiU  be  made'  in 
the  point  of  the  style  vXeinain  in  7  f  "^'  "'^""^^^  *^  ^^"'^^  tb''^^. 
length  of  time-  Ind  aTtL  n^n  ^,«"*'^«t  ^'^h  the  paper  the  same 

short  straig,™ii'nes  producer  t/-  'TY'''"''  ''^^^"^  '^^  ^^^^'  - 
dots  and  dLhes  consti  u?o  tho"  ;  .  ;  '"'"'  ^"''  ''  ^""^^  ^  ^««''-  These 
part  of  a  me  age  *  ^an  is  if" t?""  '^'T^'^"  ^"^  "^^^-->  * 
graphic  character's  'on  Te  strip  ^f  paper  ^Th  1  "  '''',"'^'  ''  ^^'«- 
interpret  their  meaning.  ^  ^  ^''™*"  ^'''"^^^  above 

Of  i,.t„„„eoL  inX^c^  r  'i:„r.r'i,r ""  "-'-'"■'■ 

that  would  move  a  sinc-ln  «^     ^"^'^-^-^^^l-     Hence,  a  current 
Wo  u>  reuder  the  message  aadlWe.     Resort  I,  V     mw 


sender,  or  oper- 

that  the  circuit 
tlie  knob  of  tlio 
iistaiitly  fills  tho 
Iraws  doAvn  the 

paper  c  that  is 
on  the  key,  the 
iper  by  a  spiral 
r  au  instant,  or 
vill  be  made  in 

to  count  three, 
paper  the  same 
ith  tho  pomt,  a 

a  dash.  These 
For  instance,  a 
riuted  in  tele- 
I  letters  above 


emoved,  and 
sharp  click  is 
piral  spring, 
the  figure), 
the  first,  is 
a  dashes  by 
tween  these 
iug  heed  to 
tie  hammer, 
rm  of  which 


the  current 
the  number 
,  a  current 
short  line, 
h  sufficieat 
1  to  relaps 
■  this  diffi. 


Plate  111. 


y 


:l 


J(| 


Relay  and  repeater.  291 

culty  may,  perhaps,  be  l.est  explained  by  analogy.    In  days  gone" 
bj,  posts   for  couriers  were   stationed  a  day's  journey  apart. 
At  each  post  were  a  courier  and  a  horse  at  all  hours  ready  to 
start       Ihe  courier,  bearing  a  dispatch,  rode  all  day,  and  at 
.ght  reached  a  post  where  fresh  houses  were  saddled  ready  for 
l.e  next  stage  of  the  journey ;  he  himself  was  exhausted^  hia 
force  was  nearly  spent,  but  he  could  awaken  a  courier  who 
was  stationed  there  and  deliver  the  despatches  to  him,  and  he 
with  fresh  strength  instantly  took  ui)  the  journey.     In  a  similar 
manner  we  picture  to  om-selves  the  electric  current  arriving  at 
a  station  so  nearly  exhausted  that  it  cannot  deliver  intelligible 
signals,  yet  it  may  still  have  strength  to  wake  up  another  bat- 
tery  and  set  in  motion  a  fresh  current  which  shall  receive  and 
announce  audibly,  or  carry  forward   the   message   which   the 
exhausted  current  has  just  strength  to  whisper. 

In  Figure  2,  Plate  III.,  the  letter  R  represents  a  relay  and  S  a  sounder 
Suppose  a  weak  current  arrives  at  New  York  from  Boston  aTd  ha" 

This   as  may  be  seen  by  examination  of  the  diagram,  will  close  another 
short  circuit,  called  the  local  circuit,  and  send  a  cun-ent  from  a  local 

Ihe  sounder  bemg  operated  by  a  battery  in  a  circuit  of  only  a  few  fee 

aiT'iH       T  *'  ""''"^'  ""'"''^-     "  ''  ''  ^^«'^^d  that  the  mes! 

age  should  go  beyond  New  York, -for  instance,  to  Philadelphia,! 
then  we  have  only  to  suppose  the  local  line  at  New  York  to  be  length- 
ened so  as  to  extend  to  Philn,'  Iphia,  and  a  powerful  line  battery  to  be 
substi  uted  for  the  small  local ,  then  the  message  that  leaves  Boston  wHl 

^ilf  .  ,  l"^""  ""'  '"■'"^*  *^  "'"  '''^''  ^*  New  York,  and  be  delivered 
ni  Philadelphia  without  the  intervention  of  any  oper'ator  on  the  route 
In  this  case  a  relay  is  called  a  repeater.     The  electro-magnets  in  relays 

Z^Z^  T  '""?■  '^"'  ""■"  "'^^'  "^"^  '''^'^  ''  --'-«  -e  wound 
vih  short,  large  wire.  (Explain.  The  main  battery  consists  of  many 
<ells ;  how  should  they  be  connected?  It  may  be  located  at  either  ter- 
minus, but  It  IS  generally  split  in  halves,  and  one  half  placed  at  each 
terminus ;  how  should  the  two  halves  be  connected  ?) 
wlVt^  v''^?'"'  *^'  '^''"^^  ''  represented  as  open  at  both  keys. 

ZZln^nf"     .T  '"  ""•  *''  ''''''''  «"^^'  *^"*>'«  t«  be  left  Closed 
by  means  of  switches  connected  with  the  keys  (not  represented  In  the 


,  ^  i-f  1 


I  ii 


1^92 


ELECTftlClTY  AND  MAGNKTlHM. 


(liagram),  so  that,  when  the  line  Is  not  "Rf  «,«  .,  .. 
-s  constantly  traversing  the  wire  trJlT"  ""  '^''''''  «""««< 
consists  in  interrupting  this  current » y  m  a„  o'f  77''  T"^^'!"^"".^ 
Boston  wishes  to  communicate  with  NewYnrU  uT  ^"^^^'^  *hat 
switch  on  his  Icey,  which  brPRk^Vh!  ,'^,^'''^-  "e  first  removes  the 
the  circuit  With  hi;  k^;  H^th  n'mal^^^^^^^^  f'^'^''  '"™  *«  -"«^«' 
an  understood  signal,  which^^llatX^vv'''':  "^"^  '"^  "'  *«  P'-^'^^ce 
time  that  Boston  presses  on  h^.\  ''  ^'"^'"  «"«ntion.     Every 

and  in  the  New  York  office  an  1  «^     ''"''^  """"'"' ^  '"  ''"  ^^'^  °^^« 

n-age  .ay  he  r.^T:e^:::,:::^z:-^^- ''  --  *^^ 


A 

sr. 

IP 

G 
M 

8 

I.                  O                    "p      ' 

S 

w 

L 
R 
X 

T 

z            '  &~ 

-  —  _ 

"  • 

•  -  •    _                                                  > 

? 

-^     . 

• 

TELEGRAPHIC  PIGURRg, 

—  -    ■ 

..!..     ._  3              4 

6 

6 

----       I'-l.."         ""'^""^ 

0 

'!! 


"itted  over  a  wire  and  appear  atTd^rj',''"'  "r"™"^'  '™- 
hand-writing  of  the  sender  a„7ll^  *"'"""'•'  '"  "■«  "^"e' 
prineiple  o/whieh  i  operateTll,  b^  f  ""T'  ""'""^-  ^he 
in  Plate  I.,  in  whieh  alfdTwL  „nto  „  ,"""  "''""  ""^  *'«^''"' 
^implieity  of  mustratbn  T^a  it  t ^  'r''7-r"  '"""«^''  *■- 
message  to  be  seat  is  written  ^itt  ,         '"'"'''  °"  ">''''''  ""o 

-ali„g.wax  in  aleobo,  The  loho  "uicr""™'  '  •'• """"""« 
the  lines  of  sealing-wax  adhetg t't I  f^rT"'"' '^'"^ 
paper  moistened  with  a  solution  of  prnssia^  „,  J  I'  I """"  "' 
^f^e  pens  is  Simply  asmail,  .K-inted^rirdr  T':,^' 
J^at  b„„  o.  the  pens  are  mo.ed  at  the  »«.„«„„„,;'  Z'Z 


THE  ELECTRIC   FIUE-ALAltM. 


093 

needle  in  New  York  to  tr  Jo  '        .  ''°'""''  "'"  """^e  the 

«.e  «eed,e  i„  Boston  tj^^     t  ^  'T"  ,"'""  '"^  ™  ^'.  ""«' 
tl.e  c-ircuit  is  broken  JTZ  ^eol'i'S-WK  on  X,  when 

'^e  there  is  a  bre^ "  UTr  "'^J  '""  ''■""•     ^'  "'"  -">= 
If,  farther,  each  n^  l"  t  7    ^"^^  "'  ""^  ""°  "™«'  »"  Y- 
'tae  it  traVe,.esttsl«v:ler/  '"''  '""'"■  '"■'" 
exaet  fae-si™i,e  of  the^  ,"   ^o         't^",""  T  ""^  "" 
chemically-prepared  paper  e^ee^    ,7,     /      V<>^"<xA  on  the 
written  in  darkSetters'o'a  ,  W  1 11'  T""'  ">»  ""S"-'  - 
in  light  letters  on  a  darkgro  ,„d      Pe      "f  .T'"""  '"  '■"'<^<^'™' 
tographs  and  other  pieffrTs  ^  v  br,"""      * ''""""''^  "' Pl^"- 
-vay.     The  pens  are  not,  ofcoZ  t,  ,"7"'"',  '"  ""*  '™« 
"ands,  bnt  by  complex  Ja  I"  ;'''x""''.S"''l^<>  "^  ""man 
■equisite  in  the  movements  otZi  ?'"'°'"  "'^"■■^tnes^ 

absolute  synchronism  i  ■  the  vib  atil™  S'T       ""7"'  "^  '"^ 
"t  each  (.rrninns.  controlled  bl.  t'eZt,;'  ^rLr'"'""''  """ 


Pig.  109. 


§  244.   The  electric   flr'*  •?! ,      n^u-     . 

of  the  electro-magnetic  teleirarh      -  /n    ""  "^^^^^^^^on 

-^.^te  the  ,eneL  plan  ^^.:.^^-^  ^ 


'If 


m 


294 


ELECTRICITY   AND  MAGNETISM. 


Prof.  M.  G.  Farmer,  and  by  him  first  introduced  into  Boston  fn 
the  year  1852. 

From  some  central  station  wires  radiate  to  every  part  of  tlio 
city.     At  suitable  intervals  there  are  inserted  in  these  circuits 
small  cottage-shaped  boxes,  usually  attached  to  buildings  at  the 
corners  of  streets.     On  opening  one  of  these  boxes,  a  person 
who  is  to  give  an  alarm  finds  a  crank  A,  which  he  is  directed  to 
"  pull  down  once  and  let  go."     This  winds  the  spring  il,  which 
sets  in  motion  a  train  of  wheels,  and  causes  a  makt-aiid-break 
wheel  C  to  revolve.     This  wheel  bears  upon  its  circumference 
notches  corresponding  to  the  number  of  the  box.    Two  terminals 
of  the  line  are  so  connected,  one  with  C  and  the  other  with  a 
lever  6,  that  when  the  lever  touches  the  wheel  the  circuit  is 
closed.    But  when  the  wheel  revolves,  and  a  notch  passes  under 
the  lever,  the  circuit  is  broken.     The  eflfect  of  breaking  the 
circuit  is  to  demagnetize  the  eleetro-m.>2  ,et  F  at  the  central 
station,  and    release   the   armature  which  is   attached   to  the 
tongue   of  a  bell.     The  tongue   then  being  drawn  forcibly  by 
the  spring  G  in  the  opposite  direction,  produces  one  stroke  on 
the  bell.     By  pulling  the  lever  down  once,  the  spring  is  wound 
up  just  pnough  to  cause  C  to  revolve  three  times,  and  thus  the 
number  of  the  box  is  struck  three  times  in  succession.     The 
watchman  at  the  central  station,  being  thus   notified  of  the 
existence  and  locality  of  the  fire,  at  once  an  .  in  a  simUar  man- 
ner notifies  the  several  fire-engine  companies. 

XXXVII.    TELEPHONE   AND  MICROPHONE. 

§  245.    Bell  telephone.  — Figure  200  represents  a  sectional  and 
a  perspective  view  of  this  instrument.     It  consists  of  a  steel  ma-net 
A,  encircled  at  one  extremity  l,y  a  spool  B  of  very  flue  insulated  wire 
tiie  ends  of  whicii  arc  connected  with  tiie  binding  screws  DD.    Im- 
mediately in  front  of  the  magnet  is  a  thin  circular  iron  disk  EE.    The 
whole  is  enclosed  in  a  wooden  or  rubber  case  F.    The  conical-shaped 
cavity  G  serves  the  purpose  of  either  a  mouth-piece  or  an  ear-trnmpet 
There  is  no  difference  between  the  transmitting  and  receivin.^  tele- 
phone; consequently  either  instniment  may  be  employed  as  a'trans- 
mltter,  while  the  other  serves  as  a  receiver.    Two  magneto  tele-honea 


o  Boston  Jn 

part  of  tlie 
lese  circuits 
lings  at  tho 
s,  a  person 

directed  to 
g  »1,  which 
>aii'l-break 
cumference 
o  terminals 
ther  with  a 
3  circuit  is 
isses  under 
caking  tlie 
tho  central 
led  to  the 
forcibly  by 

stroke  on 
g  is  wound 
d  thus  the 
jion.  The 
ed  of  the 
[uilar  man- 


BELL  TKLEPHONE. 


295 


ctional  and 
eel  magnet 
ilated  wire, 
1  DD.  Ini- 
EE.  Tlie 
ical-shaped 
ir-tnimpet. 
iving  tele- 
is  a  trans- 
telephones 


machino,  of  course  no  hattorv  ,   ''''"''  ''''^^"*'*'^  a  diminutive  magneto 


a  tuning  fork  or  the  head  of  a  drum  vibrations  ,.f 

BelUelelTno  '  \fT"''''""  "'  '''  "'^'"^^  ^"^  «'™P>-t  f-'"  o^  the 

^^tiied^^uirs^i:^,::;:,^^-  --■  -^  -at  of 

formations  and  especially  during ^^tuSio     IT tr'S 
electric    energy    through  largo  rettetaaces.    become  very  n^n?  en' 


m  '•■  I 


i    t  * 


296 


ELECTRICITY   Ax\D  .MAGNETISM. 


consists' in  inL:,      !;;\.,V:.v  it^t^  ';"i'rovcn.ont  on  the  ori,Mnal 
the   voice    instead   of  l,ei  1  o  >Ii      ?     '        "       ""^  '"  "'"''' ^'""'^  '''■'^^ 

Fig.  200  a. 


Fig.  200  6. 


ii 


disk  of  the  receiver     The  flu.  t^r  "'"'''"'"^  "'''■'^"«"«  ^"  t^t 

ance  in  the  eircuU  The  p^i  ^  71"'  ?"""?."  ^  ^"^^'"^  ^^«'«^ 
this  that  the  effect  of  a  loo  I  Ztac  50/^''"  '^  '"P^"'^^"^^  ^^« 
circuit  is  to  increase  thorlT.  "'''''''  ^"^  *^^«  P^^t^  of  a 

buttheeffec   of  a     i"    vart  r^^  '"'  *'"''^  ^^^'^'^^  "^  <=--"t; 
when  either  or  bot    of  the  pans  are"  '  h""'V'  '^''^^'^"^  "^*'^^^b^<^' 

-Pie  telephonic  circ    t    n'"  Lh  Vr  t^^^^^  '''n  "'""'"'^'^  ^ 

transmitter  T    a  mnirnpfn  Jo  ,       T  '"  ,  "''*^'^  '^  variable  resistance 

e.oc.„Ues,  a  pU.IS'tVtr.f;  r  c^^oT  L  ?";  °' ^ 
disk;  the  other  electrode,  a  carbon  button  a    TJ     *^,\*'*°«™'"er 


MICROPHONE. 


F 


■fl 


297 

R  puJls  Its   disk     Th 

The  next  iinpi-oveim.nt  of  .       f<;'"^o''"ce  sounds. 

™"  »,:'«■  ""<!  'I.«  Bell  LtmmJt   ",    ]  '°™  '""'  "  ""»  '"M- 

Pig.  201. 


§  246.   Microphon«  —  r..   i,- 
carbon;  tire  form^^S^^^XaZr^''  t  '"'  ^  "^  ''»"-«  of 
the  latter  to  a  steel  sprfn..  r  old  I    '  ^       "''"''"^^'•^'  ^^  t^in  nine  wood 

^^^r'^'""'^  any  slight  jar  will  cause  aTo^^^^  '^'■^"»  P'-^^^^^s  B 

-===:=S5;:::::; 


I 


'1 


298 


ELECTRICITY   AND  MAGNETISM. 


^.1' 


as  its  name  indicates,  sucli  as  the  ticking  of  a  watcli  or  tlie  footfall  of 
an  insect,  may  be  reproduced  at  a  considerable  distance,  and  be  as 
audible  as  though  the  original  sounds  were  made  close  to  the  ear. 


n      |l 

it"  )« 


1 


t:!]!! 


§  2466.  Storage  batteries,  or  accumulators.  —  Place 
two  strips  of  sheet-lead,  about  six  by  eight  centimeters,  at  a  distance 
of  six  centimeters  from  eacli  other,  in  a  vessel  containing  dilute 
sulphuric  acid  —  one  part  of  acid  to  ten  of  water.  Pass  the  current 
from  one  or  two  cells  through  the  liquid  from  one  plate  to  the  other, 
placing  your  short-coil  galvanometer  in  the  circuit.  You  Avill  observe 
that  the  current  grows  weaker  and  weaker,  and  finally  ceases.  When 
the  galvanometer  shows  no  current,  disconnect  the  battery,  and  connect 
the  lead  plates  with  the  galvanometer.  A  current  will  be  observed  be- 
tween the  lead  plates  in  a  direction  opposite  to  that  ,enerated  by  the 
battery.  This  is  a  polarization  current  due  to  the  generation  of  oxygen 
on  one  of  the  lead  plates  and  hydrogen  on  the  other,  by  which  a  diiler- 
ence  of  electrical  potential  is  produced. 

The  lead  cell  described  above  is  called  a  Plaute  cell,  from  the  name  of 
the  inventor.  The  Faure  cell  consists  of  lead  plates  covered  with  a 
layer  of  red  oxide  of  lead,  which  increases  the  polarization.  It  is 
evident  that  electricity  is  not  stored  in  these  cells.  A  difference  of 
chemical  constitution  is  produced,  which  in  turn  produces  a  difference 
of  electrical  potential.     What  form  of  energy  is  stored? 

These  cells,  though  greatly  improved  by  many  inventors,  have  not, 
so  far,  proved  as  satisfactory  as  was  at  tirst  hoped.  Suggest  some 
practical  applications  that  might  be  made  of  these  cells,  if  so  con- 
structed as  to  prove  efflcient  and  cheap. 


il  « 


'ootfall  of 
and  be  as 
the  car. 

3.  —  Place 
a  distance 
inj;  dilute 
he  current 
the  other, 
ill  observe 
es.  When 
nd  connect 
)served  be- 
ted by  the 
of  oxygen 
ch  a  ditt'er- 

lie  name  of 
red  with  a 
tion.  It  is 
ift'erence  of 
I  difference 

,  have  not, 

jgest  some 

if  so  con- 


CHAPTER    V. 


SOUND. 


The  subjects  of  Sound  and  Light,  which  we  have  now  to 
study,  have  two  important  characteristics  in  common  that  dis- 
tinguish them  from  tlie  subjects  already  studied.  First,  eacli  of 
them  affects  its  peculiar  organ  of  sense,  the  ear  or  eye,  and 
\ory  many  of  the  phenomena  to  be  studied  under  each  subject 
are  of  importance  only  to  one  or  the  other  of  these  senses ; 
while  the  most  common,  and  many  of  the  most  important  appli^ 
cations  of  heat  and  electricity  have  no  direct  relation  to  any 
organ  of  sense.  Second,  both  sound  and  light,  we  shall  find 
originate  in  vibrating  bodies,  and  reach  us  only  by  the  inter 
vention  of  some  medium  capable  of  being  set  in  vibration. 

Here,  as  in  all  other  kinds  of  motion,  energy  is  involved  ;  the 
ear  or  eye  absorbs  energy  whenever  a  sensation  is  produced,  but 
the  amount  absorbed  is  so  minute,  and  the  difficulty  of  measuring 
it  so  great,  that  usually  other  points  better  deserve  the  student's 
attention. 

Let  us  begin  with  the  study  of  such  vibrations  as  will  neither 
produce  sound,  nor  in  a  dark  room  affect  the  eye. 


Jl 


XXXVIII.     VIBRATION   AND  WAVES. 

§247.  Vibration.  — Experiment  1.  Repeat  the  experiment  with 
the  pendulum  1'"  long,  page  111,  and  note  in  what  respects  its  motion 
differs  from  most  other  motions. 

Experiment  2.  Take  a  pendulum  SO""  long,  hold  it  with  the  string 
just  touching  an  edge  of  a  table,  having  the  hand  about  38™  above  the 
table,  and  set  it  vibrating;  the  ball  will  be  seen  to  vibrate  faster  in  the 
portion  of  its  arc  that  Is  under  the  table  than  In  the  other  portion,  and 
so  mci-e  vibrations  are  made  In  ten  seconds  than  if  the  string  swing 
freely  without  touching  the  table. 


.ii 


300 


SOUND. 


side  to  side  every  two  seconds,  turning  instantly  at  on.-  side,  and  wait- 
ing at  the  other  till  the  two  seconds  are  up.  ^na^wait 

These  three  motions,  though  very  different,  have  this  in  com- 
mon :  the  motions  in  each  case  occnr  at  equal  intervals  of  time 
This  interval  of  time  is  called  the  period  of  vibration.    In  Exp  1 
It  was  two  seconds  ;  in  Exp.  2,  about  one  second  ;  and  in  Exp  3 
two  seconds.     The  motion  from  one  side  to  the  other  and  back 
IS  called  a  vibration.    If  n  =  the  number  of  vibrations  in  one 
second,  and  t  =  the  period,  t  =L     The  amplitude  of  pendulum 
vibrations  is  assumed  to  be  very  small.     In  Exp.  1  the  motion  is 
called  a  .tm;>/e  (or  pendular)  vibration;  in  the  other  cases  the 
v^brat^on  of  the  ball  or  the  hand  is  cample..     Do  not  confound 
period   with    duration    of  the  vibrating  state ;    in   Exp.   1  the 
pendulum   may  have  vibrated   ten    or  one   hundred   seconds, 
before  coming  to  rest,  but  the  period  was  two  seconds.     Con- 
sidered  mathematically,  other  periodic  (and  therefore  vibratory) 
motions  are,  the  movements  of  the  hands  of  a  watch,  the  regu- 
lar trips  of  a  stage-coach,  ete.    A  vibration  is  a  recurrent  channe 
of  position.  '' 

§  2«.  Direction  of  vibration.  -  A  small  rod,  like  a  yard- 
stick, fixed  at  one  end,  may  be  set  in  vibration  by  pullincr  the 
o  her  end  to  one  side  ;  a  tree  vibrates  in  the  wind  ;  the  stdncrg 
of  a  piano  swing  from  side  to  side  when  vibrating;  in  all  these 
cases  the  motion  is  at  right  angles  to  the  length  of  the  body, 
and  so  the  body  is  bent.  These  are  all  cases  of  transversi^ 
vibrations. 

hl't      '""'^Z'"''  '"^'  ^'^'  '"''  ^^^'fe'ht'  ''^"*''  ^iropping  it,  notice 
that  the  cord  vibrates,  lengthening  and  shortening  rapidly. 

The  motion  of  the  body  is  in  the  direction  of  its  length,  and 
so  It  IS  not  bent ;  this  is  a  case  of  longitudinal  vibration.  Twist 
the  strmg,  and  see  that  it  is  possible  to  set  up  torsional  vibra. 


PROPAGATION    OP    VIBRATION. 


301 


tions.     Compare  these  kinds  of  vibration  with   the   kinds   of 
elasticity  studied  on  page  30. 

§  249.  Propagation   of  vibration.  -  Waves  —  Exn..H 
meat.    Take  a  soft  cotton  rope,  a  few  meters  lon^Tay  ft*  stral^lftou 
a  floor,  sot  one  end  in  vibration  by  quick  mov^^ents  of  th?  and 
No  ice  any  po.ut  in  tixe  rope,  and  see  tliat  it  is  set  in  vibration    that 
IS,  it  moves  up  and  down,  or  laterally  from  side  to  side  tl  ough  -^ 
ongxnal  position  of  rest.     Make  a  single  movement  of  the  hand,  which 
is  better  called  a  pulse  than  a  vibration;  it  is  easy  to  see   thai    he 
pulse  does  not  reach  all  points  of  the  rope  at  the  same  t  ^e.    Send 
quick    ucces^sion  of  equal  pulses  along  the  rope;  at  any  instant  differ- 
ent pulses  affect  different  parts  of  it,  and  you  get  n.ore  o^-  less  perf  ctll 
the  famihar  form  that  we  call  a  wave-Une.     Notice  that  any  S  of 
the  rope  only  moves  up  and  down,  while  the  for^n  of  the  wave  moves 
on.     Vibm te  the  hand  in  a  longer  period,  and  notice  that  the  distance 
from  crest  to  crest  is  longer  than  before.  ui^rance 

§250.    Wave-length  and  amplitude.  -  Imagine   an   in- 
stantaneous pliotograph  taken  of  the  rope  along  which  tlie  waves 
Fig.  202.  are  passing.      It  would  appear 

much  like  the  curved  line  CD, 
Figure  202.  This  curve  repre- 
sents wliat  is  known  as  a  simple 
wave-line.  The  shortest  of  the 
similar  portions  into  which  a 
wave-line  can  be  cut  is  called  a  wave-length,  as  wx,  uv,  or  en. 
The  greatest  distance  of  any  point  in  a  wave  from  the  axis,  as 
ou,  IS  called  the  amplitude  of  the  wave. 

meitTsf^o!?f^*'°''   °f  ^aves. -Interference.' -Experi- 

and  nlu^k  it  vt  't  ."'^  Horizontally  between  two  elevated  p I.ts, 
and  pluck  it  witli  the  hand  or  strike  it  with  a  .stiek  near  one  end  and 
send  along  it  a  single  pulse,  forming  a  crest  on  the  rope  \t?l 

laverted  (B).^"^^  '  '"  ""  '^'^^  '^"•'  ""'^  "^^^  -«  -«  "  reflected  a^a 
»  See  aectlon  G  of  the  Appendij, 


E  I 


302 


STATIOXARY    VIBKATIONS,    ETC. 


r.rf«r?H""?  ^•~'^"'"  *'  '^'  '''''^'''  "^  ^^fl^^"o"  «tart  a  second 
crest;  these  two.  the  crest  and  the  returning  inverted  crest  or  trough 

(C),  are  now  traveling 
along  the  rope  in  oppo' 
site  directions,  and  must 
meet  at  some  point.  This 
point  will  be  urged  up- 
ward  by  the  crest  and 
(io\,nvvard  hy  the  trough, 
and  so  its  motion  will  be 
due  to  Mie  difference  of 
tile  two  forces. 

This  action  on  a  single  point  of  two  pulses,  or  two  trains  of 
waves,  no  matter  if  f.cui  differe.it  sources,  is  termed  interfer- 
ence.  Tlie  resulting  mo,  ion  may  be  greater  or  less  than  that 
clue  to  either  pulse  alone,  or  it  may  be  zero. 

§  252.  Water-waves.  If  you  have  a  long  and  rather 
uarrow  box  or  trough,  nearly  filled  with  water,  you  can  pro- 
duce  much  the  same  effects  as  with  the  rope.  Water-waves 
furnish  important  illustrations  of  the  fact  that  energy  may  be 
transmitted  by  vibration  as  truly  as  by  the  actual  transfer  of  the 
medium,  as  in  the  river's  current  or  the  wind. 

§  253.      Longitudinal  waves.    Experiment.   Procure  a  brass 
wire  wound  in  the  form  of  a  spiral  spring,'  about  4'"  long.     Attach  one 
end  to  a  c.gar-box,  and  fasten  the  box  to  a  table.  Hold  the  other  end    H 
of  tl.e  spiral  firmly  in  one  hand,  and  with  the  other  hand  insert  a  knife- 
Fig.  208.  blade  between  the 

turns  of  the  wire, 
and  quickly  rake 
it  for  a  short  dis- 
tance  along  the 

K^^    4.1       u  ,.  s^piral  toward  the 

box    thereby  crowding  closer  together  for  a  little  distance  (B.  Fi- 

h  M  1   *  TT  "*  "■"''  '"  '"•'"'  "^  ''•«   '•'^•^d-  ^"^  '-aving  the  turns 
behind  pulled  wider    apart  (A)    for  about  an  equal  distarce.      The 


AIR   AS   A   MKDIUM   f)F   WA VIS-MOTION.  303 

cromlcd  part  of  the  spiral  may  be  called  a  rondonmtion    and  the 
stretched  part  a  rarefaction.     The  condensatio,,  folio  v!.b":  the  rare 
facon,  runs  wUh  ^^reat  velocity  through  the  nplral,  ntrikes  the  box  pro- 

a  d  ffo^f^''   V  ""''  "  "'^^^"^  ^^'^  *"«  '-'^  ^'-'^  to  t  rha'd, 
and  from  the  hand  again  to  the  box,  producing  a  second  blow  and  by 

cssion.     If  a  piece  of  twme  be  tied  to  some  turn  of  the  wire  it  will 
be  seen  as  each  wave  passes  it,  to  receive  a  slight  Jerking   ,  o^  n 
forward  anrf  backward  In  the  direction  of  the  le.^th  of  the  spiml 

How  is  energy  transmitted  througli  these  4-  of  spring  so  as 
to  dehver  the  blow  on  the  box?  Certainly  not  by  a  bodily 
movement  of  the  spiral  as  a  whole,  as  n.ight  be  the  ease  if  it 
were  a  ngul  rod.  The  movement  of  the  twine  shows  that  the 
only  motion  winch  the  coil  undergoes  is  a  vibratory  movement 
or  Its  t.u-ns.  Here,  as  in  the  case  of  water-waves,  ener^n"  is 
transmitted  throngh  a  medium  by  the  transmission  of  vibratbns. 

There  are  two  important  distinctions  between  this  kind  of 
wave  and  a  liquid  wave  :  the  former  consists  of  a  condensation 
and  a  rarefaction  ;  the  latter,  of  an  elevation  and  a  depression  ; 
m  the  ormer  the  vibration  of  the  parts  is  in  the  same  line  with 
the  path  of  the  wave,  and  hence  these  are  called  longitudinal 
tvaves;  ,n  tue  latter,  across  its  path,  and  they  are  therefore 
transverse  waves. 

A  wavQ^cannot  be  transmitted  through  an  inelastic  soft  iron 
spiral.  Elasttcitj;  is  essential  in  a  medium,  that  it  may  transmit 
waves  made  up  of  condensations  and  rarofucflor.s;  and  the  greater 
the  elast^cuy,  the  greater  the  facility  and  rapidity  with  which  a 
medium  transmits  waves. 

§254.  Air  as  a  medium  of  wave-motion.  -  May  not  air 
and  other  gases,  which  are  elastic,  serve  as  m.-dia  for  waves? 

20r^LT*r,r*:,^'''''  "  '*"''^°  ''"'""  '^^  *''°  '''^^''  ^  "f"  the  tube,-  FWnire 
20G,  and  strike  the  table  a  sharp  blow  with  a  book  near  the  orlQco  I 

made  .U.htly  tapCng.  .o  that  tl.ey  „«,•  b^  pi.t  to'^tb      ,        '.  o  "JpV"^'  "'''''  '^ 


i  : 


S04 


SOUND. 


Instantly  the  candle  flame  Is  quenched      Th«  h  a      . 
serves  as  a  medium  for  transmhsW^n  nf"       .        ""^^  "^  ''^'  *"  ^^^  t"he 
Was  it  the  motion   '''"''""■^■^'"'^  of  motion  to  the  candle. 

blown  throu,hr;;?i  .rr:^;/;T  ""-'^^''  '''  tu.e,.s.Ue. 
touch-paper,  at  the  oriflce  h,  so  a  to  flfl  ^'"''7'  """°"'  «»- 
smoke,  and  repeat  the  last  experiment  ''^     ''  *'^°  *"^«  ^^^^l^ 

smSitiutlSed:;^:',:^;;:;"^;:'^  ^'t  "^^"^'^ «»« *'^^«'  «- 

but  no  smoke  issues  fron^th    o^flce  ^    Tt"  i      f  ""V^  ^"*  "^^  '''^^^' 

onnce  a.     It  is  clear  that  fchere  is  no 

Fig.  208. 


»pnug  ,s  ,0  p,.„,u,ce  in  a  certain  section  (flt  20      oC 
M>..al  a  crowding  together  of  the  t,„™  o    wi  ■  °™,  I  a 
xei)avat,ou  ;  but  the  elastioitv  of  the  soiral  ZJZ'       -       ^  " 

wa.  .no^nent  orritirr^^^^^^^ 

"Otall:  the  folds  in  the  sect  o,  «  >  .""""  "^"=-  '''''''  '» 
when  they  have  recoveJt L  on 'ir  loT  '"  f'"  ^^"' 
pendnlu.,  swing  heyond  the  po  itl^  f  oT  .e'^ 'tZ'  Z'  '"'  " 
.-faction  at  B,  where,  immediately  befor:!' thT:  T,  HoV 


in  the  tiibe 
le. 

be,  as  when 
;ion?  Burn 
;  tube  with 

e  tube,  the 
t  as  before, 
*liere  is  no 


—nothing 
by  some- 

ledium. 
e  spiral 
)  of  the 
at  A  a 
ies  B  to 
3ther  of 
3  a  for- 
e  same 
Jtion  at 
rhis  is 

swinir 

like  a 

icing  a 

a  con- 

eacnpfhJ 
'per  pro- 


SOtTND-WAVES. 


305 


densation.     Thus  a  forward  movement   of  th.  .      ■ 

made,  and  thus  a  nnl^p  «..      ^'^^^^"'^   °^  *he   rarefaction   is 

XXXIX.     WAVE-SOUNDS. 

sen...,.  J,  :::l'  -  ;,i:r  i::z  n:r"  '"^ 

of  the  impression  mado  on  tl.o  ear      But  2  Tn  ""'""^ 

distanee  that  it  cannot  itself  act  on  tl,!ear    vet    1  ".r  ""■■"  " 
act  o.^,.  .,.,  and  it  .nst  .  the  .e,,  Sir  ttt^ - 

Hrr::r^i:^:i----j.„i,,., 

against  t^ebeV     wtft^ tbe  r  I  ^tV%'?,:;;^^^  Press  the  hand 

fork,  press  the  stem  against  a  abl     vn  '  ^"'"'^'  ^^  "^  *""'«-'- 

the  Cheek  with  the  .naT::^^^^^  VCt  th^^"f  ^^'""^ 
prongs  just  beneath  the  surface  of  water  wZ'fl"  T^'  °'  '^' 
piano,  guitar,  or  viohn  or  the  tnn.,L    7    ■  "'*"  ^^""^'«  ^f  a 

From  the  above  exoeriments  ,:  ^J  :eii;^;;^^^^^^^  ^^^  -""^i"..- 
in  motion?  What  kind  of  motio.^"  IIow  loo.  t.  •  '''""'"""  "^"^'^  ^' 
that  which  we  caU  Ixeat?  Ho  v  does  it\lt';  ""« '"^*^««  differ  from 
projectile?  ^^"^^  **  ^''"^'^  f»*om  the  motion  of  a 

^o:::::^:t;;,:':trnX:  t:-t:^  t  r  -' 

V  bratinn  •  wb-.-.  -    '  -  a,  state  of  contmuoijs 

part,rf;.etd;reT::-;::— ;:r 

that  »o„«i  <,„v,«a,e»  i,  a  .ibrating'l^!^!^  ^''  ™"°"«"' 


J 


Ill 


IN 


306 


SOUND. 


il  a     H 


So,md,   that   proceed   from  the  tM„i„K.|brk  and  tbe  violin 
«tn„g  are  example,  of  ,„„nd  produeed  l.y  t„u„ver,e  vihratior 

a.ul  gra^p  ,„„  tube  tightly  „,th  thi.,  ha,,.,,  „,„    '"Z      ZZ'lZ' 

J'ZTZu  ^iJ"""  '  '""•  "'  ""'*"""  "'  '"■'"'  '»•"  Ions  and 
o     iMUc,  make  a  hole  near  one  e,i<l,  and  »ii»,>i.m,i  h,  ,,  ,„,„„  ,„  , 

from  the  hand,  and  rotate  It  rapidly  ahont  th,    l,a„l  a    ,        f  " 

o  a  ,l,„g     The  string  will  rapldly'twl,.  a„d',;„  ,"     ."J  ^^ ^^ZZ 

will  result  from  the  tovsional  eitralloai. 

§257.  How  sound  travels.  -  IIow  „„„  „  l,„||,  ^^„^- 
at  a  distance,  affect  the  cur?     If  the  1,„||  „hilo  ,o„,  din.  po" 
sesses  no  peouhar  propc-t,-  except  ,„„ti.,„.  ti„.„  it  „„,  ZthZ 
to  coramuinca  c  to  .he  ear  l,nt  motion.     n„t  „,„ti„„   ean  b°c 
corn,n„„,cated  by  one  body  to  anotb,.-  „t  a  distance  only  thron.d! 
some  medium.  -^  """"»" 

Does  sound  require  a  medium  for  it.  co.umunicution  ?    If  so 
what  IS  the  medium  ?  ' 

Experiment.    Lay  a  thick  tuft  of  cotton-wool  on  fhn  nlnf„  ^f 
a.-pu,„p  and  on  this,  face  downward,  piace  alo  a?t  c  tg"^^  ch  a" 
cover  with  the  receiver.     Notice  tliat  the  receiver  UttlrZJnT. 
the  watch  and  your  ear.  greatly  diniiniHlLrl  r^oSo^  „  :  ^r:: 
with  the  passage  of  somHhing  to  the  ear.    Tako  a  few  stLes  of  th. 

lb  he  ;rrhe::^  ^t^f^^  Progre^Hen.  „„tn  citherL  Im  d 
cau  De  heard  when  the  ear  i.s  placed  close  to  tlio  receiver  or  nn  nv 
tro^ely  faint  one,  as  if  coding  from  a  great  dl«ta„"  T.'.c  relv':; 
of  air  from  a  portion  of  the  space  botwee,,  tho  watch  and  vom-lr 
.  estroys  the  sound,  although  the  watch  continues  to  t^k  let  ^  he 
air  again  and  the  sound  is  restored. 

Thus  it  appears  that  soM/i(^  cannot  travel  th  mm,],  n  ..ocw^n  ■  ir 
oti^er  words  .«/^Ao«;  a  mer/m,n,  and  the  mcdn.m  in  this  case  is  air 
Jiy  which  of  the  two  methods  described  in  §  254  is  mo- 


AIR-WAVES. 


807 


If 


so. 


tion  transmitted  from  the  sounding  body  tlirough  the  nir?    Take 
an  extreme  case :  A  cannon  is  discharged  at  a  distance  of  one- 
fourth  of  a  mile  from  you.     You  not  only  hear  the  sound,  but 
fee    tiie   shock   communicated   by  the   air ;   the  windows   are 
shaken  by  it ;  at  tl)e  same  time,  you  easily  perceive  that  it  is 
not  the  motion  of  a  wind,  but  the  motion  of  a  pulse      It  can 
easily  be  shown  that  the  pulse  travelled  at  a  rate  of  about  800 
miles  in  an  hour,  or  with  nearly  the  velocity  of  a  rifle  ball 
whereas  the  wind  of  a  hurricane  seldom  exceeds  75  miles  an 
hour.     What,  think  you,  would  be  the  result  if  you  were  ^o  be 
struck  by  a  gust  of  wind  of  such  velocity?     Yet  the  softest 
Avlusper  travels  with  very  nearly  the  same  speed. 

§258.    Air-waves.  — Boys  amuse  themselves  by  inflatins 
paper  bags,  and  with  a  quick  blow  bursting  them,  producing 
with  each  a  single  loud  report.     First  the  air  is  suddenly  and 
greatly  condensed  by  the  blow,  the  bag  is  burst ;  the  air  now,  as 
suddenly  and  with  equal  force,  expands,  and  by  its  expansion 
condenses  the  air  for  a  certain  distance  all  around  it,  leaving  a 
rarefaction  where  just  before  had  been  a  condensation.     If  many 
bags  were  burst  at  the  same  spot  in  rapid  succession,  the  result 
would  be  that  alternating  shells  of  condensation  and  rarefaction 
would  be  thrown  off,  all  having  a  common  center,  enlar^ring  as 
they  advance,  like  the  waves  formed  by  stones  dropped  into 
water;  only  that,  in  this  case,  the  waves  are  not  like  rings,  but 
hollow  globes  ;  not  circular,  but  spherical. 
^    As  a  wave  advances,  each  individual  air-particle  concerned  in 
Its  transmission  performs  a  short  excursion  fro  and  to  in  a 
straight  line  radiating  from  the  center  of  the  shells  or  hollow 
globes.     A  particle  begins  to  move  when  the  front  of  the  shell     • 
of  compression  touches  it,  and  completes  its  motion  when  the 
back  of  the  next  shell  of  rarefaction  leaves  it.     Accordincrly  an 
air-wave  travels  its  axon  length  in  the  time  that  a  particle  occupies 
in  going  through  one  complete  vibration  so  as  to  be  ready  to  start 
again. 


I 

Sll 

m 


Mfl 


1 


308 


SOUND. 


„Jif     ;    Y^'"'''^  is. -The    term  «o««rn8  sometimes 
.ntnf  >  '  ^^"••'^^^•'^"'^^'"^"tiraes  to  denote  the  external 

cause  of  I.e  sensaU.,,. ;  it  is  in  this  latter  sense  that  the  word  is 
nsed  ni  Piiys.es,  and  that  we  have  to  define  it. 

If  the  ear  replu'O  the  cai...lle  ii.  the  experiment  (§  254),  the 
a.r.pnlse  prodnees  a  loud  sound.  Air-waves  started  by  the  voice 
may  affect  a  flame.  In  fact,  the  relation  between  the  cause  of 
oursensation  and  a  vibration  is  so  uniform  that  we  may  say 
6onndu  viljrnUon  that  may  be  appreciated  by  the  ear.  Accord  - 
•ng  to  this  definition,  is  the  vibration  in  the  metal  of   a  ringii.. 


{ii 


M 


§260.  Sohds  and  liquids  as  media  transmitting  sound 
-  Expenment  1.    Lay  a  watch,  with  its  back  downward,  on  and  near 

?old  f"  /:  '•  r-^  '"'''  ^"'  '''^''^'  -^"^  --''•  t'-  vvat  h  With  loose 
folds  of  cloth  tdl  us  ticking  cannot  be  heard  through  the  air  in  am 
direction  at  a  distance  equal  to  the  length  of  the  board.  Novv  plac  • 
the  ear  m  contact  with  the  distant  end  of  the  board. 

Experiment  1.     Place  one  end  of  a  long  pole  on  the  sounding-boani 
of^a  p.ano,  and  apply  the  stem  of  a  vibrating  tuning-fork  to  the  oth^! 

Experiment  3.  Place  the  ear  to  the  earth,  and  listen  to  the  rumbling 
of  a  distant  carnage;  or,  put  the  ear  to  one  end  of  a  long  stick  of  tim 
ber,  and  let  some  one  gently  scratch  the  other  end  with  a  pin. 

Experiment  4.  The  following  experiment  will  be  found  verv  in 
structive  and  satisfactory :  Let  two  persons  stand  about  fifteen  rods 
apart,  and  one  of  them  strike  two  pel,ble-stones  together  .so  as  to  be 
scarcely  audible  to  the  other.  Then,,  when  at  the  same  distance  apart 
let  one  of  them  d've  to  the  bottom  of  a  pond  of  water,  or  hold  one  I; 
for  a  few  seconds  beneath  the  surface  of  the  water,  while  t]ie  other 
ex  ..nding  his  hands  into  the  water,  strikes  the  stones  togethe  as 
before.       Describe  the  result  in  each  of  as  many  of  the  above  and 

Solids  and  liquids,  as  well  as  gases,  transmit  sound  vibra. 
twns. 


VELOClTir   O'^   SOUND. 


309 


>  sometimes 

he  external 

the  word  xs 

;§  254),  the 
>y  the  voice 
lie  cause  of 

may  say, 
.     Accord - 

a  ringing 
ve  call  the 


ngr  sound. 

on  and  near 

li  with  loose 

e  air  in  any 

Now  placo 

idlng-boanl 
0  the  other 

le  rumbling 
ick  of  tim- 
1. 

id  very  in- 
Ifteen  rods 
so  as  to  be 
xnce  apart, 
)Id  one  ear 
the  other, 
ogether  as 
ibove  and 
elusion  do 


XL.  VELOCITY  OF  SOUND. 
§  26L  On  what  velocity  of  sound  depends.  -  The  flash 
of  a  gun  however  distant,  is  seen  by  an  observer  at  the  instant 
It  IS  made  But  the  report,  if  the  distance  is  several  hundred 
yards  IS  heard  a  little  later.  If  the  distance  is  a  mile,  an  in- 
terval of  nearly  five  seconds  will  occur;  so  that  sound  mu.t 
occupy  that  time  in  traveling  a  mile,  or  it  must  travel  about 
1100  feet  m  a  second, -a  velocity  somewhat  less  than  that  of 
a  rifle  ball. 

It  is  apparent  that  sound  must  travel  more  slowly  in  a  dense 
than  m  "  rare  medium,  inasmuch  as  in  the  former  there  is  a 
greater  mass  to  be  moved;  on  the  other  hand,  it  travels 
faster  m  the  medium  that  is  the  most  elastic.  Densitu 
retards  and  elasticity  increases  the  velocity  of  sound.  The  rela- 
tion of  velocity  to  the  density  and  elasticity  of  gases,  as  ascer- 
tamed  by  careful  experiment,  is  as  follows  :  the  velocity  of  sound 
in  gases  ts  directly  proportional  to  the  square  root  of  their  elasti- 
city,  and  inversely  propoHional  to  the  square  root  of  their 
respective  densities. 

ssl^'nm^t,"'  ""'  i°  'r  '*  '°^-  '^^  ^«^"  ^--^  ^  b« 

333    (1093  ft.)  per  second.     Its  velocity  increases  nearly  six- 
tenths  of  a  meter  for  each  degree  centigrade.     At  the  temper- 

Tt    .  S'^'r  ^''^^-^  "^  "^^  ^^^^^^  *^«  -I«-ty  of  sound 
at  about  342™  (1125  ft.)  per  second. 

The  greater  density  of  solids  and  liquids,  as  compared  with 
gases,  tends,  of  course,  to  diminish  the  velocity  of  sound ;  but 
their  greater  elasticity^  more  than  compensates  for  the  decrease 
of  velocity  occasioned  by  the  increase  of  density.  As  a  general 
rule,  solids  are  more  elastic  than  liquids  ;  hence,  sound  generally 
travels  faster  m  the  former  than  in  the  latter.     For  example 


sound  travels  in  water  about  4  times  as  fast  as  in 

"The  question  will  very  perUnently  ariae  here,  inwrauch  as  gases  are   nerfprtJ 
eUuitlcHowcao  solids  and  Ilqulda  be  regarded  as  having  greater  elSu'    iTshmd 
^understood  that  whUe  gases  completely  recover  thL%olume  aftl  ^  coinp^^^^^^^ 
force  is  rerooved,  they  do  it  more  ■luygi.bly  thao  .olidi  and  UquJdi.  *=*""P««»°8 


'}| 


'If 


810 


SOUND. 


(r 


4  times;  m  gold,  5  times;  iu  brass,  10  times;  in  copper,  11 
times;  m  uon,  16  times;  in  glass,  16  times;  in  wood  aiong 
ihe  fiber  between  10  and  15  times;  in  wood,  across  the  fiber! 
between  4  and  6  times. 

QUESTIONS. 

affe^ted?^  /see  Til'  f  5m  It  ^'^^P^^^^^^''  ^«^  '«  ^^s  density  or  volume 
anected?  (See  §  12o.)  (b)  How  is  its  elasticity  affected?  (c)  How  is  it 
affected  as  regards  the  velocnty  witi.  which  ,t  w.ll  transnnt^sou^.T 

2    Hydrogen  Is  sLxteeu  times  lighter  (or  rarer)  than  oxygen  under 
he  same  pressure.     (.)  m  which  will  sound  travel  fasterpT^)  Why 
(c)  How  many  times  faster?  (.«;  wnyr 

3.  When  sound  travels  in  air  with  a  velocity  of  331-  per  second  it 
travels  .„  carbonic  acid  gas  at  the  rate  of  262™  per  second  (a)  Which 
IS  the  denser  gas  ?(&)  How  many  times  denser? 

4.  When  a  confined  body  of  air  is  heated,  it  has  its  elasticity  in- 

sTn  of  sound?"'  "'  '''"""  "'  ''""'^-    ^'''  ^"^  '""'^  ^«"-'  *^^-™»"- 
6.   If  air  is  heated  and  allowed  to  expand  freely,  as  on  a  warm 
summer  day,  its  elasticity  is  unaffected,  but  its  density  is  diminirhed 
how  will  this  affect  the  triusmission  of  sound^  cluninished . 


XLI.  REFLECTION  AND  REFRACTION  OF  SOUND. 

§262.  Reflection.— In  the  experiment  with  the  spiral 
spring,  waves  wore  reflected  from  the  box  to  the  hand,  and 
from  the  hand  to  the  box.  When  a  sound-wave  meets  an 
obstacle  in  its  course,  it  is  reflected  ;  and  a  sound  heard  after 
being  thus  reflected  is  often  called  an  echo,  or  reverberation  when 
many  times  reflected,  so  that  the  sound  becomes  nearly  con- 
tinuous. 


§  263.    Sound  reflected  by  concave  mirrors.  —  Experi- 

ment.  Place  a  watch  at  the  focus  (page  286)  A,  Figure  208,  of  a  con- 
cave mirror  G.  At  the  focus  B  of  another  concave  mirror  H.  nlaop  th- 
.argcupcn.ngof  a  small  tunnel,  and  with  a  rubber  connector  attach 
the  bent  glass  tube  C  to  the  noM-  of  the  tunnel.  The  extremity  D 
being  placed  iu  the  ear,  the  ticking  of  the  watch  can  be  heard  very 


in  copper,  11 
I  wood,  along 
•osa  the  fiber, 


isity  or  volume 
'   (c)  How  is  it 
lit  sound? 
oxygeu  under 
er?     (6)  Why? 

per  second,  It 
Id.    (a)  Which 

s  elasticity  in- 
flect transmia- 

is  on  a  warm 
is  diminished ; 


I  the  spiral 
e  hand,  and 
e   meets   an 

heard  after 
sration  when 

nearly  eon- 


s.  —  Experl- 

108,  of  a  con- 
r  H,  place  the 
lector  attach 
extremity  U 
e  heard  very 


REFLECTION   AND   REFRACTION.  311 

distinctly,  as  though  it  were  somewhere  near  the  mirror  II.  Though 
the  mirrors  be  5n>  apart,  the  sound  will  be  heard  much  louder  at  B  than 
at  an  intertermediate  point  E. 

How  is  this  explained?  Every  air-particle  in  a  certain 
radial  line,  as  Ac,  receives  and  transmits  motion  in  the  direc- 
tion  of  this  line ;  the  last  particle  strikes  tlie  mirror  at  c,  and 
being  perfectly  elastic,  bonnds  off  in  the  direction  cc'  in  con- 
formity to  the  law  of  reflection  (§87),  communicating  its 
motion  to  the  particles  in  this  line.  At  c'  a  similar  reflection 
gives  motion  to  the  air-particles  in  the  line  c'B.  In  consequence 
of  these  two  reflections,  all  divergent  lines  of  force,  as  Ad,  Ae, 

rig_208.  ^^*^"'  ^''^*^  ^^^^  *'^^  mirror 

Q  {/ vj        ^'»    Jire     tliere     rendered 

A^,"  parallel,    and   afterwards 
hi    rendered    convergent    at 
'    the  mirror  II.    The  prac- 
tical result  of  the  concen- 
tration of  this  scattering 
^  .  .  force  is,  that  a  sound  of 

great  intensity  is  heard  at  B.  The  points  A  and  B  are  called 
the  foe.  of  the  mirrors.  The  front  of  the  wave  as  it  leaves  A 
18  convex,  in  passing  from  G  to  H  it  is  plane,  and  from  II 
to  B  .oncave.  If  you  fill  a  large  circular  tin  basin  with 
water,  and  strike  one  edge  with  a  knuckle,  circular  waves  with 
concave  fronts  will  close  in  on  the  center,  heaping  up  the 
water  at  that  point.  t-    o     f 

ciJr^p"''^''^'""^"^'"'''''''"  ^^^«  ^^«"  constructed  on  this  prin- 
ciple    Persons  stationed  at  the  foci  of  the  concave  ends  of  theZ. 

fw  eTcarotr^^"":  conversation  in  a  whisper  which  persons  be"- 
tween  canno  hear.  A  most  notable  instance  was  that  of  the  "  Ear  of 
Dionysius,"  in  the  dungeon  of  Syracuse.     The  roof  of  the  p-ison  was 

to  the  ear  of  the  tyrant,  even  the  whispers  of  the  victims  tliere  con- 

behTnH  .?*'™^l'^'  ^"  "■  "''""'^  condenser.  The  hand  held  concave 
behind  the  ear,  by  its  increased  surface,  adds  to  its  efficiency.    An  ear 


iF 


tii 


■  §1 


312 


SOUND. 


rig.  209, 


4  distant,  and  thea  introduce  a  collodion  balloon  B  filled  with 
earbomc  acid  gas  between  your  ear  and  the  watch,  and  "  y 
near  the  latter,  the  sound  becomes  much  louder.  ^ 

The  cause  is  obvious ;  for,  let  the  curved  lines  a  b  r  ^to    ..r. 
sections  of  sound-waves  with  convex  frontrand  «  «^     ^■'    Tf'"^ 
of  carbonic  acid  gas  which  is  dcn^c^-  Z^Z^tTXll    h^aT 
owing  to  the  slower  progress  of  the  waves  1^  the  den  er  2    U.ev 

Zts  'r  Te  T"'.  °°  ^"^""'-"  ^^'^  ''^''  -^  *^«  ^^ZoTlo^Z 

ironts  may  be  changed  to  waves  of  plane  front<i      A,roin        ,   '"®* 
the  .«re™i«es  of  the  wave.,  having  Ici  .Ustan™  fo  ,™t  "„'  .Sfd  L" 
gas  than  points  near  the  center,  would  emor-e  (tr«f  «„h  „  ,  ■  '"V""''" 

as  It  progressed,  Is  so  ehanged  In  direction  In  passing  mto  and  o,  fot 

:ir;Lrrtr;:?;>:r;rtei^^^^^^ 


Any  change  in  direction  of  sound,  caused  by  passing  from  a 


ite,  at  the  small 
Iter  at  the  large 


the  small  end 
of  a  watch  A, 


B  filled  with 
3h,  and  very 

itc,  represent 
pherlcal  body 
is  clear  that, 
ser  gas,  they 
es  of  convex 
in,  points  at 

in  the  denser 
it  in  advance, 
in  the  dense 

the  form  of 
ning  (iimised 

less  intense 
'  and  out  of 
icentrated  at 


sing  from  a 
nt  density, 


.LOUDNESS. 


813 


XLII.    LOUDNESS   OF   SOUND. 


§    _65  Loudness  depends  on  amplitude  of  vibrations 
Gentry  tap  the  prong,  of  a  tuning-fork  and  dip  them  i.t  wate7 

tTo  bir     .r  T"  ■     "'^"^  '''  ^'^^"'"  '  "---«  the  fo  "of 
the  blow,  — the  vibrau..,s  become  wider  ind  thn  ^nf 

thrown  with  greater  foree  and  to  a  grelt^ dll;:^^^^^^^^ 
lung  occurs  when  the  fork  vibrates  in  air;  thou^^h  we  do  Tot 
s  e   the  a,r.partieles  as  they  are  batted  b;  the  moving  Jo" 
yet  we  feel  the  effects  as  a  sound  sensation,  and  we    u^d.e  o^ 
their  energy  by  the  intensity  of   the  sensat  on      T  '  h    °       I 
sound  is  really  the  measure  of  a  sens.t  o"    b^n  '^"'''  "' 

suitable  or  constant  standard  of  ::::^^^\:  Z^^:: 
we  are  compelled  to  measure  rather  the  intensity  oMe^un  ' 
wave,  knowing  at  the  same  time  that  the  loudness  n'r  " 
portional  to  this  intensity;  unfortunately  the  expres  Lns  /  " 
ness  and  intensity  of  sonnrl  are  often  intorchan '^c  7^  ? 
s.ty  of  a  vibration  is  measured  by  the  en^ty^o  "the  ,/?"" 
particle.  It  is  clear  that  if  the\amplitI^'or  vitat  n;"? 
V^  IS  doubled  while  its  period  roniins  const^,t"l^t: 

^^..ssor  intensity  of  ^)^r^-^  Z!^^^ 
of  the  amphtude  of  the  vibrations  of  the  sounding  body 

dinm  ^^'  Loudness  depends  upon  the  density  of  the  me- 

dum.-In  the  experiment  with  the  watch  undei   the  ite^'r 

the  air-pump   (§257),    the  sound  grew  feebler  as    he  air 

no  e  to  make  their  conversation  heard  when  they  reach  are-it 
nghts  than  wh..  in  the  denser  lower  air.     Fill  a'g  aTsbefl  H 
with  hydrogen  ga.,  and  place  in  it  a  small  alarm  clodc     tj^ 
sound  is  exceedingly  weak   and  thin    „a  ''""  ^^^ck  ,  the 

„„     J     ,         .  °^  ^   "^^^   '^"'"i  as  compared   with  thp 

sound  when  the  jar  is  filled  with  nir      ri.  - 

us   (9\  thr,t  ii     '  .         "^^'  ^^"'"  ^"-      ^''ese  experiments  teaoh 
us,  (2)  that  the  vntensity  of  sound  depends  upon  the  density  of 


lll'l 


ll;i 


314 


SOTTND. 


111 


it 


I 

if     ■ 

m 


the  medium  in  which  it  is  produced.  In  a  rare  medium  a  vibrat- 
ing body  during  a  single  vibration  sets  in  motion  either  fewer 
particles,  as  in  the  case  of  the  partially  exhausted  receiver,  or, 
as  in  the  case  of  the  hydrogen  gas,  it  sets  in  motion  lighter  par- 
ticles than  in  a  dense  medium;  consequently  it  parts  with  its 
energy  more  slowly,  and  the  sound  is  consequently  weaker. 

(In  which  ought  the  vibrations  of  a  body  to  last  longer  —in 
a  dense  or  in  a  rare  medium ?    Why?)  ' 

§  267.   Loudness  depends  on  distance. -It  is  a  matter 
of  every-day  observation  that  the  loudness  of  a  sound  dimin- 
ishes very  rapidly  as  the  di^ance  from  its  source  to  the  ear 
increases.    The  ear  is  not,  however,  able  to  compare  very  accu- 
rately the   loudness   of  two   sounds ;    for  instance,  it  cannot 
determine  when  one   sound  is  just  twice  as  loud  as  another. 
This,  however,  so  far  as  it  is  affected  by  distance,  can  be  very 
accurately  determined  by  calculation.     For  it  is  evident  that  as 
a  sound-wave  recedes  from  its  source  in  an  ever-widening  sphere 
a  given  amount  of  energy  becomes  distributed  over  an  ever- 
increasing  surface ;  and  as  a  greater  number  of  particles  par- 
take of  the  motion,  individual  particles  receive  proportionally 
less  energy ;  hence  it  follows,  -as  a  consequence  of  the  geomet- 
rical truth,  that  the  surface  of  a  sphere  varies  as  the  square  of  its 
radius,  — that  (3)  the  intensity  of  sound  varies  inversely  as  the 
square  of  the  distance  from  its  source.    For  example,  if  two  per- 
sons, A  and  B,  are  respectively  500  and  1000  meters  from  a  -run 
when  It  IS  discharged,  the  report  that  reaches  A  will  be  four 
times  as  loud  as  the  same  report  when  it  reaches  B. 

§  268.  Speaking  tubes.  —  Experiment.  Place  a  watch  at  one 
end  of  the  long  tin  tube  (Fig.  200),  and  the  o  u-  at  the  ot'rr  end  tL 
tickmg  is  heard  very  loud,  as  though  the  watch  were  close  to  the  ear. 

Long  tin  tubes,  called  ^.aJ^-ing  tubes,  passing  through  many 
apartments  in  a  building,  enable  persons  at  the  distant  extremi- 
ties  to  carry  on  conversation  in  a  low  tone  of  voice,  while  per- 


ium  a  vibrat- 
either  fewer 
receiver,  or, 
lighter  par- 
arts  with  its 
weaker, 
longer,  —  in 


is  a  matter 
5und  dimiu- 
!  to  tJie  ear 
G  very  accu- 
!,  it  cannot 
as  another, 
can  be  very 
lent  that  as 
ling  sphere, 
er  an  ever- 
irticles  par- 
)portionaIly 
the  geomet- 
quare  of  its 
rsely  as  the 
if  two  per- 
f  rom  a  gun 
ill  be  four 


DISTINCTION  BETWEEN  NOISE   AND  MUSIC.  315 

IZZ'"""  ^f '"'  '°°'"'  '''°"°^  ^^^^^  ^^«  ^"^«  P^««««  hear 


notbin 


Ihe  reason    is  the  sound-waves  which   enter 


-  --    ._  ™„  .^»^i..i«-»T«vca  wiucn   enter    the 

tube  are  prevented  from  expanding,  consequently  the  intensity 
of  sound  IS  not  affected  by  distance,  except  as  its  energy  is 
wasted  by  friction  of  the  air  against  the  sides  of  the  tube. 

Tf  !w^'i  ^;^*^°,°.^^°°  b«*^««^  noise  and  musical  sound. 
If  the  body  that  strikes  the  air  deals  it  but  a  single  blow,  like  the 
discharge  of  a  firecracker,  the  ear  receives  but  a  single  shock 
and  the  r.,ult  is  called  a  noise.     If  several  shocks  a're  ^1 
recr  .,y  the  ear  in  succession,  the  ear  distinguishes  them 

as       ..^ay  separate  noises.     If,  however,  the  body  that  strikes 
the  air  is  ui  vibration,  and  deals  it  a  great  number  of  little  blows 
m  a  second,  or  if  a  large  number  oi  '^.re-crackers  are  dischar^^ed 
one  after  another  very  rapidly,  so  that  the  ear  is  unable  to  dis- 
tmguish  the  individual  shocks,  the  effect  produced  is  that  of  one 
continuous  sound,  which  may  be  pleasing  to  the  ear ;  and,  if  so 
It  IS  called  a  musical  sound.     But  continuity  of  sound  does  not 
necessarily  render  it  musical.     The  sound  produced  by  a  hun- 
dred  children  beating  various  articles  in  a  room   with  clubs 
might  not  be  lacking  in  continuity,  but  it  would  be  an  intoler- 
able noise.     There  would  be  wanting  those  elements  that  please 
the  ear;  viz.,  regularity  both  in  periodicity  and  intensity  of  the 
shocks  which  it  receives.     The  distinction  between  music  and 
no.se  IS,  generally  speaking,  a  distinction  between  the  agreeable 
and  the  disagreeable,  botween  regularity  and  confusion.      The 
charactensucs  of  a  musical  sound  are  regularity  and  simplicity. 


vatch  at  one 
r  end.  The 
to  the  ear. 

)ugh  many 

it  extremi- 

while  per- 


116 


SOUND. 


m  I 


XLIII.     PITCH   OF    SOUNDS. 

§  270.  On  what  pitch  depends.  —  Draw  the  finger-nail 
slowly,  and  then  rapidl}',  across  the  teeth  of  a  comb.  The  two 
musical  sounds  produced  are  commonly  described  as  low  or 
grave,  and  higJt  or  acute,  and  the  higlit  of  a  musical  sound  is 
called  pitch.  What  is  the  cause  of  a  difference  in  hight  or 
pitch  of  two  sounds? 


Fig.  215. 


Experiment.  Procure  a  circular  sheet-iron  or  pasteboard  disk  A, 
Figure  21.",,  SO-^'"  in  diameter.  Prom  tlie  center  of  the  disk  describe  a 
circle  with  a  radius  of  12'='".  Iq  the  circumfer- 
euce  of  this  circle,  with  a  punch,  cut  holes  S"™ 
in  diameter,  leaving  equal  intervals  of  about  2="" 
between  the  holes.  Insert  in  a  rubber  tube  a 
piece  of  glass  tube  B,  of  l^m  bore,  drawn  out  at 
one  eud  so  that  its  orifice  is  about  i"^  jq  diame- 
ter. Attach  the  disk  to  some  rotating  apparatus, 
hold  the  small  orifice  of  the  glass  tube  opposite 
the  holes,  and  blow  steadily  through  the  tube, 
and  rotate  the  disk  at  first  very  slowly  and  then 
with  gradually  increasing  rapidity.  The  breath, 
as  it  makes  its  exit  f  i-om  the  tube,  cannot  escape 
continuously  through  the  holes,  but  is  cut  up  by 
the  passing  obstructions  into  a  series  of  puffs, 
which  at  first  are  heard  as  so  many  distinct 
sounds;  as  the  speed  increases,  the  number  of 
puffs  in  a  second  increases,  until  the  ear  can  no 
longer  separate  them,  when  they  blend  together 
?n  a  deep  sound  of  a  definite  pitch. 

The  peculiarity  of  tliis  instrument  is  that  it  does  not  produce 
sound  by  its  own  vibrations.  Every  time  the  air  is  driven 
through  a  hole,  it  produces  a  pulse  of  condensation  in  the  air 
beyond;  and  during  the  interval  between  the  successive  dis- 
charges, a  pulse  of  rarefaction  will  be  caused  by  the  elasticity  of 
the  air,  so  that  the  result  is  the  same,  so  far  as  the  effect  on 
the  air  medium  is  concerned,  as  if  a  body  were  vibrating 
in  it.     As   the  velocity  increases,  the  pitch  constantly  rises, 


LIMITS   OF  THE   SCALE   AND    IIIOAItlNO. 


ai7 


i    finger-nail 

L).     The  two 

i  as  low  or 

3al  sound  is 

in  hight  or 


oard  disk  A, 
ik  describe  a 
13  circumfer- 
cut  holes  S™" 
1  of  about  2="' 
ubber  tube  a 
drawn  out  at 
tmm  in  diame- 
ig  apparatus, 
ube  opposite 
gh  the  tube, 
tvly  and  then 
The  breath, 
anuot  escape 
;  is  cut  up  by 
les  of  puffs, 
any  distinct 
e  number  of 
le  ear  can  no 
3nd  together 


until,  at  the  greatest  speed  conveniently  attainal)l(;,  it  boeomes 
painfully  shrill.  Varying  the  force  of  the  breath  affects  the 
loudness  of  the  sound,  but  does  not  affect  itH  pitch. 

So  we  liave  discovered  the  important  fact  that  pitch  depends 
upon  Vibration-frequency  or  wave-length,  i.e.,  the  greater  the 
number  of  vibrations  per  second,  or  the  shorter  the  wave-length, 
the  higher  the  pitch.  If  the  number  of  vibrations  per  second 
18  doubled,  the  pitch  is  raided  one  octave. 


QUESTIONS   AND    EXERCISES. 
1.    Why  does  the  same  bell  always  give  a  sound  of  the  same  pitch? 

f  '^'  ,  ^"l^.^^^"  '•'  "'''  ^^^^*  "^  '^"'''"«  "^  '^^'"  "'ll''  <"i"'"-<-nt  degrees  of 
force?  (6)  What  change  in  the  vibrations  is  productcd?  (c)  What 
property  of  sound  remains  the  same? 

8-     (a)  Strike  a  key  of  a  piano,  and  liold  It  down ;  what  is  the  only 

frSn  ^^^  "1^'"^^  "'  **"'  '"""^  P''^^^"'"^^^  ^'"'«  "'  '•^"•"^»n«  audible? 
(6;  What  is  the  cause  of  this  change? 

4.  Rake  tlie  teeth  of  a  comb  with  a  flngcr-iiall,  at  llrst  slowly,  then 
quickly,  and  account  for  the  dittbrence  in  the  characfr  of  the  sounds 
produced. 

«•     (a)  On  what  does  pitch  depeiul?     (i)  ()„  ,vhat,  loudness? 


i  I 


lot  produce 
r  is  driven 
in  the  air 
iessive  dis- 
ilasticity  of 
16  effect  on 
!  vibrating 
.ntly  rises, 


§  271.  Limits  of  the  scale  and  hearing.  —  The  lowest 
note  of  a  7J  octave  piano  makes  about  27i,  tlio  highest,  4  2->4 
vibrations  per  second;  but  these  extreme  notes  have  little 
musical  value,  and  the  lowest  notes  are  only  used  for  their  har- 
monies.  The  range  of  the  humaii  voice  11'.-.  bf-twoen  100 
and  1,000  vibrations  per  second,  or  a  little  more  than  three 
octaves;  an  ordinary  singer  has  ah--^  the  compass  of  two 
octaves. 


318 


SOUND. 


il  > 


The  ear  is  capable  of  hearing  vibrations  far  exceeding  in 
number  the  requirements  of  music.     It  can  appreciate  sounds 
arising  from  32  to  38,000  vibrations  -  per  second,  i.e.,  a  ran^e 
ofabout  eleven  octaves,  and  a  corresponding  range  of  wave- 
length between  seventy  feet  and  three  or  four  tenths  of  an  inch 
These  numbers  vary,  however,  considerably  with  the  person, 
it-xceptional  ears  can  hear  as  many  as  50,000  vibrations.    Some 
ears  can  hear  a  bat's  cry,  or  the  creaking  of  a  cricket ;  others 


i 


XLIV.   VIBRATION   OF   STRINGS. 

§  272.     Sonometer. -Experiment.     Take  a  piece  of  violin- 
stnng  or  piano-wire  a  little  longer  than  your  table.     Fasten  one  Ind  to 

p.     218  ^  "*"  '"  °"*^  ^"'^  ^^  *^e 

table,  and  pass  the  other 

end  over  a  pulley  fastened 

to  the  other  end  of  the 

table,  and  to  this  end  of 

the  string  suspend  a  pail 

containing  sand,  the  two 

weighing  just   a   pound. 

Place    under    the  string, 

near  the  ends  of  the  table, 

A  and  B  rFijr  91s^      a  .       ,  <^^vo  ^vedge-shaped  bridges 

Pln.wi,  ,■'  ^.lu  ^  apparatus  thus  arranged  is  called  a  sonomefer 
r  uck  the  stnng  with  the  fingers  near  the  middle,  causing  It  to  vibrate 
a^d  note  the  pitch  of  the  sound,  and  the  length  of  the  string  between 
the  bridges.   Movc  the  bridge  A  toward  B ;  the  pitch  rises  as  tie  v  ^rat 

S7s  r;    T  ^*'"^  ^^  ^'"'^"^'^'-     ^^'•y''-  position  o    A  uSa 

ound  ha^  tT  .  T  ""'""'  "''"'  ""  P"^'^  ^'''"^  ^'  «r«*'  «»d  it  Will  be 
found  that  the  string  is  just  one-half  its  original  length  •  i  p    A«  h., 

the  string  its  vibration-number  is  doubled.  ^    '        '  *^  '^"''''*"^ 

Now,  increasing  the  weight  in  the  pail,  the  pitch  rises,  till,  when  the 

tension  IS  four  pounds,  the  pitch  has  risen  an  octave.     Let^he  ten! 

sujnbe  the  same ;  try  another  string,  weighing,  for  the  samelen.^ 

results.)  "^  experiments  wiU  not  give  very  accurate 

» Preyer  place,  the  lowe.t  limit  for  some  e«n  at  18  vibration,  per  woond. 


exceeding  in 
reciate  sounds 

*.e.,  a  range 
nge  of  wave- 
ihs  of  an  inch. 
ti  the  person, 
ations.  Some 
icket;  others 


iece  of  violin- 
iten  one  end  to 
ne  end  of  the 
jass  the  other 
Julley  fastened 
^r  end  of  the 
to  this  end  of 
mspend  a  pail 
!iand,  the  two 
ist   a   pound, 
r    the  string, 
s  of  the  table, 
ihaped  bridges 
d  a  sonometer. 
:  it  to  vibrate, 
tring  between 
as  thevibrat- 
n  of  A  until  a 
and  it  will  be 
e. ,  by  halving 

till,  when  the 
Let  the  ten- 
same  length, 
that  given  by 
ery  accurate 

Moond. 


QUALITY  OF  SOUND. 


319 


These  conclusions  may  be  summarized  by  saying :  T7ie  vibra- 
tion-numbers of  strings  of  the  same  material  vary  inversely  as 
their  lengths  and  square  roots  of  their  weights,  and  directly  as  the 
square  roots  of  their  tensions. 


1. 

ing? 


GocSTIONS  AND  PROBLEMS. 

Why  does  a  violinist  finger  the  strings  of  the  violin  when  play- 


2.      Examine  the  strings  of  a  piano,  and  ascertain  the  different 
methods  by  which  a  wide  range  of  pitch  is  effected. 

8.      How  does  the  length  of  the  string  that  gives  the  note  F  compare 
v/ith  the  length  of  the  C-string  below  it,  other  things  being  equal? 


XLVL    QUALITY  OF  SOUND. 

Let  the  same  note  be  sounded  with  the  same  intensity,  suc- 
cessively, on  a  variety  of  musical  instruments,  e.g.,  a  violin, 
cornet,  clarinet,  accordion,  jews-harp,   etc. ;  each  instrument 
will  send  to  your  ear  the  same  number  of  waves,  and  the  waves 
from  each  will  strike  the  ear  with  the  same  force  ;  yet  the  ear  is 
able  to  distinguish  a  decided  difference  between  the  sounds,  — 
a  difference  that  enables  us  instantly  to  identify  the  instruments 
from  which  they  come.     Sounds  from  instruments  of  the  same 
kind,  but  by  different  makers,  usually  exhibit  decided  differences 
of  character.     For  instance,  of  two  pianos,  the  sound  of  one 
will  be  described  as  richer  and  fuller,  or  more  ringing,  or  more 
"  wiry,"  etc.,  than  the  other.     No   two  human  voices  sound 
exactly  alike.     That  difference  in  the  character  of  sounds,  not 
due  to  pitch  or  intensity,  that  enables  us  to  distinguish  one 
from  another,  is  called  quality.     Two  sounds  may  differ  from 
one  another  in  loudness,  pitch,  or  quality;  they  can  differ  in  no 
other  respect. 


nt 


ii", 


'I 


320 


SOUND. 


Pitch  depends  on  frequency  of  vibrations,  loudness  on  their 
amplitude  ;  on  what  does  quality  ,/epm,l? 

§  273.     Analysis  of  sounds.  -  Tl.«  u.mkled  ear  is  unable,  ex- 
Fig.  220,  •'«'l"' <«"i  very  limited  extent,  to 

diHtliiKuish  the  individual  tones 
tliiit  <;onipose  a  note.  Ilelmholtz 
«n-tti)«t;(l  a  series  of  resonators 
fOHMlutlng  of  liollovv  spheres  of 
l>niM»,  each  having  two  openings  : 
<nw  (A,  Fig.  220)  large,  for  the 

reception  ofthe  sound-waves,  and 
tli«  other  (B)  small  and  funnel- 
shaped,  and  adapted  for  inser- 
tion Into  the  ear.  Each  reson- 
ator of  the  series  was  adapted 

aTlr  ;  JT'  "'  T'"  ^'^^'""^^"'•«'  t"«  ^•'^r,  placed  at  the  orifice  of 

any  one  ,s  able  to  single  out  f rou.  a  c-olh-.tlon  that  overtone,  if  present 

to  Which  alone  this  resonator  is  capa..,«  of  rcHpouding.      t  is  found 

hat,  when  a  note  is  produced  on  a  give,  Instrument,  not  only  is  there 

Sip-— isrr--^,r=i£ 

note  can  ,;e  formed  at  that  point;  <-on«.'r,uontlv  fhc  two  im.,^  I     . 
ovmonc.  produced  b,  2  .„.,  4  «„» C;      ,,  So/o    ™ 

g  "  rX'"  „r;,e:  '™""r',    .'""'«"  "'  <•"«-•   vlcCetc 
fcencrall,  .ti  utk  uoar  <„io  of  tlii-lr  e„,l«,  aii.l  lliii,  thoy  are  doprivid  of 
only  some  of  their  hlsLei-  aud  feebler  overtone..  "'•Pr'vstI  "1 


ess  on  their 


is  unable,  ex- 
ted  extent,  to 
lividual  tones 
e.  Helmlioltz 
)f  resonators 
vv  spheres  of 
wo  openings: 
arge,  for  the 
Kl-waves,and 

I  and  funnel- 
id  for  iuser- 
p]ach  reson- 
was  adapted 

II  powerfully 
cal  sound  is 
he  orifice  of 
e,  if  present. 

It  is  found 
3nly  is  there 
,  but  all  the 

Which  are 
the  point  of 
3  middle,  no 
)  important 
;ions  of  the 
3,  etc.,  are 
deprived  of 


CHAPTER  VI. 
RADIANT  ENERGY. -LIGHT. 


L.  INTRODUCTION. 

§  274.  Lightaformof  energy.  — Exposed  to  the  sun,  the 
skin  is  warmed,  and  thus  the  sense  of  touch  is  affected  ;  it  is 
iUuminated,  and  thereby  the  sense  of  sight  is  affected ;  it  is 
tanned,  and  thereby  its  chemical  condition  is  changed.  It  is  evi- 
dent that  we  receive  something  which  must  come  to  us  from  the 
sun.  To  the  sense  of  touch  it  appears  to  be  heat ;  to  the  eye 
it  is  light ;  to  certain  substances  it  is  a  power  to  produce  chemi- 
cal changes.  But  what  is  it  that  we  receive 
from  the  sunf 


Fig.  234. 


Experiment — Blacken  one-half  of  one  side  of  a 
slip  of  glass  with  candle-smoke.  With  a  convex 
lens,  sometimes  called  a  "  burning-glass,"  converge 
the  sun's  light  upon  the  blackened  portion  so  as  to 
produce  a  small  luminous  spot  on  the  black  surface. 
This  spot  quickly  becomes  very  hot,  but  the  lens 
meantime  remains  comparatively  cold.  Move  the 
luminous  spot  to  the  unblackened  portion  of  the 
glass.  The  spot  becomes  only  slightly  heated. 
Place  a  piece  of  paper  behind  and  in  contact  with 
the  glass,  and  It  quickly  burns.    > 

Whether  we  receive  heat  from  the  sun  or 
not,  it  is  evident  that  we  receive  something 
that  can  be  converted  into  heat. 

Figure  234  represents  an  instrument  called 
a  radiometer.    The  moving  part  is  a  small  vane  resting  on  the 
pomt  of  a  needle.     It  is  so  nicely  poised  on  this  pivot  that  it 


■ill 


322 


RADIANT  ENERGY.  —  LIGHT. 


5   ■ 


rotates  with  the  greatest  freedom.  To  the  extremities  of  each 
of  the  four  arms  of  the  vane  are  attached  disks  of  aluminum 
which  are  white  on  one  side  and  l)lack  on  the  other.  The  whole 
is  enclosed  in  a  glass  l.nlb  from  which  the  air  is  exhausted  till 
less  than  ^r^^  of  the  original  (luantity  is  left.  If  the  instrument 
is  exposed  to  the  sun's  light,  or  even  to  the  light  of  a  candle, 
the  wheel  will  rotate  witli  the  unblackened  faces  in  advance. 

In  just  what  manner  it  is  caused  to  rotate  does  not  concern 
us ;  but  the  fact  that  it  does  rotate,  and  that  it  is  caused  to 
rotate  directly  or  indirectly  by  something  that  comes  froin  the 
sun  or  the  candle,  is  pertinent  to  the  question  before  us.  When- 
ever  a  body  is  caused  to  move  or  increase  its  rate  of  motion, 
energy  must  be  imparted  to  it ;  hence  energy  must  be  imparted 
to  the  radiometer-vane  by  the  sun  or  candle. 

Bell,  the  inventor  of  the  telephone,  has  succeeded  in  produc- 
ing musical  sounds  by  the  action  of  sun-light  and  other  intense 
lights.  But  sound  always  originates  in  motion,  and  motion 
springs  only  from  some  form  of  energy.  So,  then,  that  which  toe 
receive  from  the  sun,  tvhether  it  affects  the  sense  of  touch  and  is 
called  heat,  or  the  eye  and  is  called  light,  or  produces  chemical 
changes  and  is  called  chemism,  is  in  reality  some  form  of  energy. 

§  275.  Ether  the  medium  of  motion.  —  If  light  is  motion, 
wiiat  moves  ?     Our  atmosphere  is  but  a  thin  investment  of  the 
earth,  while  the  great  space  that  separates  us  from  the  sun  con- 
tains  no  air  or  other  known  substance.     But  empty  space  can 
neither  receive  nor  communicate  motion.     It  is  assumed  — lY  is 
necessary  to  assume  — that  there  is  some  medium  filling  the 
interplanetary  space,  in   fact,  filling  all  otherwise  unoccupied 
space  (i.e.,  where  matter  is  not,  ether  is),  by  which  motion 
can  be  communicated  from  one  point  in  the  otherwise  empty 
space  to  another.    This  medium,  has  received  the  name  of  ether. 
Ether  is  supposed  to  penetrate  even  among  the  molecules  of 
liquid  and  solid  matter,  and  thus  surrounds  every  molecule  of 
matter  in  the  universe,  as  the  atmosphere  surrounds  the  earth. 


tTNDULATORY   THEORY  OP   LIGHT. 


323 


nities  of  each 
of  aluminum 
'.     The  whole 
exhausted  till 
le  instrumenli 
;  of  a  candle, 
advance. 
3  not  concern 
is  caused  to 
les  from  the 
e  us.    When- 
te  of  motion, 
1  be  imparted 

id  in  produc- 
>ther  intense 
and  motion 
'hat  which  toe 
touch  and  is 
ices  chemical 
1  of  energy. 

it  is  motion, 
ment  of  the 
the  sun  con- 
y  space  can 
iraed  —  it  is 
I  filling  the 
unoccupied 
lich  motion 
wise  empty 
tne  of  ether. 
lolecules  of 
Tiolecule  of 
3  the  earth. 


No  vacuum  of  this  medium  can  be  obtained;  an  attempt  to 
pump  it  out  of  a  space;  would  be  like  trying  to  pump  water 
with  a  sieve  for  a  piston.  We  cannot  see,  hear,  feel,  taste, 
smell,  weigh,  nor  measure  it.  What  evidence,  then,  have  we 
that  it  exists  ?  You  believe  that  a  horse  can  see ;  you  have  no 
absolute  knowledge  of  the  fact.  But  you  reason  thus :  he  be- 
haves as  if  he  could  see  ;  in  other  words,  you  are  able  to  account 
for  his  actions  on  the  hypothesis  that  he  can  see,  and  on  no 
other.  Phenomena  occur  just  as  they  would  occur  if  all  space 
were  filled  with  an  ethereal  medium  capable  of  transmitting, 
motion,  and  we  can  account  for  these  phenomena  on  no  other 
iiypothesis  ;  hence  our  belief  in  the  existence  of  the  medium. 

The  transmission  of  energy  through  the  medium  of  ether  is 
called  radiation;  energy  so  transmitted  is  called  radiant  energy, 
and  the  body  emitting  energy  in  this  manner  is  called  a  radiator. 
Sound  is  another  form  of  radiant  energy  transmitted  through 
solid,  liquid,  or  gaseous  media.  ^ 

§  276.  Undulatory  theory  of  light.  — Is  motion  commu- 
nicated  by  a  transfer  of  a  medium  or  by  a  transfer  of  vibrations, 
I.e.,  by  undulations  ?  All  evidence  points  to  one  conclusion! 
that  we  receive  energy  from  the  sun  in  the  form  of  vibrations  or 
wave-action;  that  these  vibrations,  inaudible  to  our  ears,  cause 
through  the  eye  the  sensation  of  sight,  and  through  the  hand  the 
sensation  of  warmth.  This  is  known  as  the  undulatory  theory  of 
light.  To  learn  what  the  special  evidences  of  the  correctness 
of  this  theory  are,  the  pupil  must  wait  for  further  development 
of  our  subject ;  but  it  should  be  borne  in  mind  that  the  strongest 
p>oofof  the  correctness  of  any  theory  is  its  exclusive  competence 
to  explain  phenomena.  Light  is  vibration  that  may  he  appre- 
ciated by  the  organ  of  sight. 

§  277.     Ray,  beam,  pencil.  —  Anv  line.  R  R.  FiaurP  935 
which  pierces  the  surface  of  a  wave  of  light,  a  b,  perpendicularly 
IS  called  a  ray  of  light.     It  is  an  expression  for  the  direction 
in  which  motion  is  propagated,  and  along  which  the      ocessive 


i     I  4 


S24 


.;    I 


UADIANT   ENEHdV.  —  LIOTrT. 


ii:  I 


effects  of  liglit  occur.     If  the  wave-surface  a'  b'  is  a  plane,  the 
rays  R'  R'  are  parallel,  and  a  collection  of  such  rays  is  called  a 

beam  of  light.  If  the  wave-surface 
a  6  18  spherical  or  concave,  the 
rays  R"  R"  have  a  common  point  at 
the  center  of  curvature,  and  a  col- 
lection of  such  rays  is  called  r 
pencil  of  light. 

§  278.    Seeingr    an    object.  — 
When  a  pencil  of  light  enters  your 
eye    you    experience     a    sensation 
which  leads  you   to  the  conclusion 
that  a  particle  of  matter  lies  at  the 
point  of  intersection  of  the  rays  of 
the  pencil,  and  you  say  that  you  see 
a  paiticle  of  matter  at  that  point. 
The  reasoning  by  which  you  reach 
this  conclusion  is  the  result  of  ex- 
perience ;  and,  since  you  go  through 
this  process   of    reasoning    uncon- 
sciously, it  is  called   unconscious  reasoning.     If  your  eye  is 
turned  towards  a  caudle-flame,  a  pencil  of  light  enters  your  eye 
from  each  particle  of  the  flame,  and  the  sensation  experienced 
leacj  you  to  conclude  that  a  particle  of  matter  lies  at  the  poin- 
in  which  the  rays  of  each  pencil  of  light  intersect.     The  ag- 
gregation of  these  particles  constitutes  the  flame,  and  you  arc 
led  to  say  that  you  see  the  flame.     From  this  explanation  it 
will  be  seen  that,  when  you  say  that  you  see  a  certain  object  in 
a  certain  position,  you  have  experienced  the  sensation  arising 
from   pencils  of  light  entering  your  eye,  just  as  if  they  had 
emanated  from  all  the  points  in  an  object  so  situated,  and  had 
travelled  m  straiglit  lines  to  your  eye.     If  a  uniform  medium 
such  as  the  air  at  the  surface  of  the  earth  usually  is,  lies  be- 
tween your  eye  and  the  luminous  object,  the  ra\8  of  light 


SEEING   AN  On-FECT. 


825 


do   travel   .n   straight   lines,    .and  you    sec    the   object   where 
it    actually    m.      I5ut   if    by   any    means    the    rays  of    li^ht 
emanating    from    a    luminous    object    have    their   directions 
changed  before  entering  your  eye,  of  course  the  sensation  is 
changed   and  yon  do  p  .  ..e  the  object   where  it  actually  is. 
If,  nfter  the  change  oi  dir.aion,  the  rays  of  light  enter  your 
eye  just  as  they  woul  i  ..t.r  it    "  they  emanated  from  the  points 
of  .some  object  m  a  .h  .ad  po  .tion,  and  travelled  in  straight 
Imes  to  your  eye,  you  s.     ,;>.  object  in  this  second  position,  or, 
asjt  ,s  commonly  expressed,  you  see  .nn  image  of  the  object. 
Hut  If,  after  the  change  of  direction,  the  rays  of  light  enter 
your  eye  as  they  could  not  enter  it  if  they  emanated  from  the 
pomts  of  any  possible  object  in  any  possible  position,  and 
ravelled  in  straight  lines  to  your  eye,  you  do  not  see  anything, 
that  IS,  your  experience  does  not  enable  you  to  draw  any  con- 
clusion from  the  sensation. 


i. .  ■ 

I 


ine  particles  of  the  flame  on  the  side  towards  your  eve  give  rise  to 

rnence  in  straight  lines  to  your  eye.     lu  consequence  of  the  sensation 

the  Sor'  *'sle:"'^^^'  T  ^^"  ^^^  ^'^  ^^^^'^^  the  Le  S  nd 
the  mirror.      Sometimes,  guided  by  other  senses,   or  judginff    from 

previous  experience,  you  may  be  able  to  determine  wl  ether  you  ar^ 


I 


RnHiVfl  o.«  *         '  -^-^■"^""S"".  aud  opaque  bodies.— 

Hodies  are  transparent,  translucent,  or  opaque,  according  to  the 
manner  in  which  they  act  upon  the  Iuminife;ou.  wavet  wh  ch 
pass  thix>ugh  them.     Generally  speaking,   those  objects  are 


m 


326 


RADIANT    ENERGY.  —  LIGHT. 


transparent  that  allow  other  objects  to  be  seen  through  them 
(hstinctly  ;  e.g.,  air,  glass,  and  water.  Those  objects  are  trans- 
lucent  that  allow  light  to  pass,  but  in  such  a  scattered  condition 
that  objects  are  not  seen  distinctly  through  them;  ea  fo" 
ground  glass,  and  oiled  paper.     Those  objects  .^.^p^Z  Z 

r  r^rz.'^" ''- ''''  -^  ^--  ^^--  ^-  ^ 

§  280.  Liuninous  and  illuminated  objects.  _  Some  bodies 
are  seen  by  means  of  light,  which  they  generate  and  emit  ,e^, 
he  sun,  a  candle  flame,  and  a  -live  coal";  they  are  called 
lurninous  bodies  Other  bodies  are  seen  only  ^y  me'ans  of  ^ 
which  they  receive  from  luminous  ones,  and  when  thus  rendered 
visible,  are  said  to  be  illuminated;  e.g.,  the  moon,  a  man,  a 
cloud,  and  a  "dead  "coal. 

§  281.  Every  point  of  a  luminous  body  an  independent 

source  of  light. -Place  a  candle  flame  in  the  center  of  a 

darkened  room;   every  wall    and 

every  point  of  each  wall  becomes 

illuminated.     Place   your  eye    in 

any  part  of  the  room,  i.e.,  in  any 

direction  from  the  flame ;  it  is  able 

to    see    not  only  the  flame,  but 

every  point  of  the  flairs;  hence 

every  point  of  the  flame  must  emit 
light  in  every  direcaon.     Every 

point  of  a  luminous  body  is  an  in- 
dependent source  of  light  and  emits 
light  in   -very  direction.     Such  a 

point  is   called  a  luminous  point.      In  Figure  2Sfi  thorn 
represented  a  few  of  the  infinite  number  ^"s  of  liZ 
emitted  .y  three  luminous  points  of  a  n„ndle  l^Tt  w 

of^an  illuminated  object  ab  receives  light  frtreverTl^rr 


IMAGES    FORMED. 


327 


!♦  282.  Images  formed  through  small  apertures.  -  Ex- 
P«Kment.--Cut  a  hole  about  Sen  square  in  one  side  of  a  box;  cover 
the  uole  with  tin-foil,  ana  prick  a  hole  iu  the  foil  with  a  pin.  Place  the 
box  ,ri  a  darkened  room,  and  a  candle  flame  in  the  box  near  to  the  pin- 
hole. Hold  an  oiled-paper  screen  before  the  h.xe  in  the  foil.  What  do 
you  observe?    Can  you  account  for  the  phenomenon? 

If  light  from  objects  illuminated  by  the  sun  — e.^.,  trees, 
houses,  clouds,  or  even  an  entire  landscape  —  is  allowed  to  pass 
through  a  small  aperture   iu  a  window  shutter  and  strilce  a 
wlilte  screen,  or  a  white  wall  in  a  darlc  room,  rays  carrying  with 
them  the  color  of  the  points  from  which  they  issue  will  imprint 
their  own  color  on  the  screen,  and  inverted  images  of  the  objects 
in  their  true  colors  will  appear  upon  it.     The  cause  of  those  phe- 
nomena is  easily  understood. 
When  no  screen  intervenes 
between  the  candle  and  the 
screen  A,  Figure  237,  every 
point  of  the  screen  receives 
liglit   from   every   point    of 
the  candle  ;  consequently,  on 
every  point  on  A,  images  of 
the  infinite  number  of  points 
of  the   candle   are   formed. 
The  result  of  the  confusion  of  images  is  equivalent  to  no  image, 
lint  let  the  screen  B,  containing  a  small  hole,  be  interposed ;  then, 
since  light  travels  only  in  straight  lines,  the  point  Y'  can  only 
receive  an  imago  of  the  point  Y,  the  point  Z'  only  of  the  point 
Z,  and  so  for  intermediate  points  ;  hence  a  distinct  image  of  tlio 
object  must  bo  formed  oa  the  screen  A.     Tliat  an  image  may  b ; 
distinct,  the  raj/ s  from  different  points  of  the  object  must  not  mix 
on  the  image,  but  all  rai/s  from  each  point  on  the  object  must 
be  carried  to  its  otvn      '  -       ■'     • 


t^JOO 


image 


(« 


■Hi: 


!     i. 


328 


EADIANT  ENERGY LIGHT. 


QUESTIONS. 
l'  wu^  ^e  images,  formed  through  apertures.  Inverted? 
2.   Why  ,8  the  size  of  the  image  dependent  on  the  distance  of  fho 
screen  from  the  aperture?  uihtance  of  the 

8.    Obtain  the  dimensions,  respectively,  of  an  obiect  anri  if=  . 
and  their  respective  distances  from  the  fntervening  sere"     ZT^"^^ 
tarn  the  law  that  determines  in  aU  cases  the  size  o?anTma";  ""- 

5    Whv  T"  ""  T?'"  '"'""^^  ^™"^^^  ««  ''  becomes  larger? 

7    wTatTr^"^''' '''''' °"'^"°*^^^^*''^«»t  interfering? 
7.   What  fact  does  a  gunner  recognize  in  talking  sight? 

i 
§  283.    Shadows.  —  Experiment  1.    Procnrp  tw«  «.^ 
or  card-board,  one  ISc^  square,  tl.  other  3^^  s^^  p^^  ^^^^^ 
between  a  white  wall  and  a  candle  flame  in  a  darkened  ron^     IT 
opaque  tin  intercepts  the  light  that  strikes  it    and  then-hv        ,  I" 
light  from  a  space  bcliind  it  '  ^"^"^^  ^''^^"^^'^ 

This  space  is  called  a  shado^.o.  That  portion  of  the  surface 
of  the  wal  that  is  darkened  is  a  section  of  the  shadow Xl 
eprcsents  the  form  of  a  section  of  the  body  that  intereep  s  the 
hg It  A  section  of  a  shadow  is  frequently  for  convenience 
cal  ed  a  shadow.  Notice  that  the  shadow  ll  made  up  o  tw" 
distinct  parts,  -a  dark  center  bordered  on  all  sides  by  a  mudi 
lighter  fringe.  The  dark  center  is  called  the  «..6raf  and  t 
hghter  envelope  is  called  the  jienumbra. 

Experiment  2.  Carry  the  tin  nearer  the  wall,  and  notice  that  ih^ 
penumbra  gradually  disappears  and  the  outline  of  the  mnbri  become 
.nore  distinct.    Employ  two  candle  flames,  a  little  distance  apartl^ 
no^^ice  that  two  shadows  are  produced.     Move  the  tin  toward  ^wa 

Lthis?  "''^  "''''"P  ''''  ^''"^'^^  ^"^  deepest.     Why 

Just  so  the  umbra  of  every  shadow  is  the  part  that  gets  no 
hyht  from  a  luminous  body,  tohile   the  penumbra  is  the  part 


I 
t 
b 
c 
e 
ii 


SHADOWS. 


829 


that  gets  light  from  some  poHion  of  the  body,  hut  not  from 
the  whole.  '' 


Experiment  3.     Repeat    the  above  experiments,  employing  tlie 
smaller  piece  of  tin,  and  note  all  differences  in  phenomena  that  occur 

Hold  a  hair  in  the  sunlight,  about  a 
centimeter  in  front  of  a  fly-leaf  of  this 
book,  aud  observe  the  shadow  cast  by 
the  hair.  Then  gradually  increase  the 
distance  between  the  hair  and  the  leaf, 
and  note  the  change  of  phenomena.  If 
the  source  of  light  were  a  single  luminous  point,  as  A,  Figure  238  the 
shadow  of  an  opaque  body  B  would  be  of  infinite  length,  and  would  con- 
sist only  of  an  umbra.  But,  if  the  source  of  light  has  a  sensible  size, 
the  opaque  l)ody  will  intercept  just  as  mauy  separate  pencils  of  light  as 
there  are  luminous  points,  and  consequently  will  cast  an  equal  number 
of  mdependent  shadows. 

Fig.  239. 


n 


bodv  Th'  ^'^"  ff  ^'  ^^P'-^^^"*  «  lu'^^nous  body,  and  CD  an  opaque 
body.  The  pencil  from  the  luminous  point  A  will  be  intercepted  Z 
tween  the  lines  C  P  and  D  G,  and  the  pencil  from  B  will  be  ntcrcepted 
between  the  lines  CE  and  DP.  Hence,  the  ll^ht  wHl  b'  Tc^T"^ 
eluded  only  from  the  space  between  the  lines  CF  and  DP    which 

included  between  the  lines  CE  and  CP,  and  between  DP  amlDG 
receives  light  from  certain  points  of  the  luminous  body,  but  not  from  all' 


;!H 


330 


EADIANT  ENERGY.  —  LIGHT. 


QUESTIONS. 

m^rfS^""  '^"  ""''"■''  ^°^  ^'""™^''*  '^*  ""^  ''''  «P*1»«  body  HI. 

2.  Wht  5  will  a  transverse  section  of  an  umbra  of  an  opaque  bodv  h^ 
larger  than  the  object  itself?  ^^      ^^^  ^^ 

3.  When  has  an  umbra  a  limited  length? 

4.  What  Is  the  shape  of  the  umbra  cast  by  the  sphere  C  D,  Figure  239  ? 
6.   If  CD  should  become  the  luminous  body,  and  A  B a  non-fuminous 

^aque  body,  what  changes  would  occur  lu  the  umbra  and  the  sTZw 

6.  Why  is  it  difficult  to  determine  the  exact  point  where  the  umbra 
of  a  church-steeple  terminates  on  the  ground? 

7.  What  is  the  shape  of  a  section  of  a  shadow  cast  by  a  circular  disk 
Placed  o^,hquely  between  a  luminous  body  and  a  screen?  What  is  its 
shape  when  the  disk  is  placed  edgewise? 

h„?„  '^f'  f «««°  of  the  earth's  umb.a  on  the  moon  'n  an  eclipse  always 


Fig.  240. 


LI.     PHOTOMETRY. 

§284.  Law  of  inverse  squares.  -  Experiment  l.  Arranjre 
apparatus  as  follows :  Lay  a  silver  half-dollar  on  the  center  of  a  cS 
lar  p,ece  of  stiff,  white,  unglazed  paper  of  15cm  diameter,  and  rub  the 
entire  surface,  except  the  portion  covered  by  the  coin,  with  a  sperm  or 
a  tallow  candle.     Hold  the  paper  in  a  warm  oven  for  a  minute.     When 
the  paper  is  placed  between  two  lights  in  a  darkened  room,  the  un- 
greased  spot  will  appear  light  on  a  dark  background  on  the  side  which 
receives  the  more  light,  and 
dark  on  a  light  background 
on  the  side  which  receives 
less  light ;  but  the  spot  be- 
comes     nearly      invisible 
when  both  sides  are  cqu.il- 
ly   illuminated.      Draw   a 
straight  chalk  line  across 
a  table,  and  place  at  right  

.    ,  „  n,njjic  iignced  caudle.     Ra^f-v/av  hpfw..Pii  fhio 

m    It  ,s  endem  thai  „-e  M,  „f  tu  paper  receives  fo„  tLe^tto 


ue  body  HI, 
^ue  body  be 


Figure  230? 
3n-luminous 
the  shadow 

3  the  umbra 

Lrcular  disk 
iVhat  is  its 

ipse  always 
le  shape  of 


I.  Arrange 
of  a  circu- 
ad  rub  the 
a  sperm  or 
te.  When 
'm,  the  un- 
hide which 


the  same 
rveeu  this 
in  Figure 
times  the 


PHOTOMETRY.  gc^j 

light  that  the  other  does.     M..ve  the  row  of  lights  slowly  awav  from 

c  foun  in  either  case  where  the  spot  will  nearly  disappear.  Wha^  is 
the  p:,s,tion  of  the  paper  with  respect  to  the  two  sources  of  light  when 
this  occurs?    What  do  you  infer?  "a  iifcni  wnen 

Thus,  by  doubling  the  distance,  the  intensity  of  illumination 
18  diminished  four-fold.  In  a  similar  manner  it  may  be  shown 
that  at  three  times  the  distance  it  takes  i.ine  lights  to  be  equiv- 
alent to  one  light.  Hence,  the  intenaity  of  light  diminishes  as 
the  square  of  the  distance  increases.  Tliis  is  callea  the  law  of 
inverse  squares. 

Experiment  2.  Introduce  the  paper  disk,  as  above,  between  a 
candle  light  and  a  kerosene  light  or  a  gas  flame,  and  so  regulate  the 
distance  that  the  central  spot  will  disappear,  and  calculate  the  relative 
intensities  of  the  two  lights  in  accordance  with  the  law  of  inverse 
squares. 

Apparatus  arranged  for  this  irposo  is  called  a  photometer. 
'The  candle  power,  which  is  the  unit  of  light  generally  em- 
ployed m  photometry,  is  the  amount  of  light  given  by  a  sperm 
candle  weighing  one-sixth  of  a  pound,  and  burning  one  hundred 
and  twenty  grains  an  hour."  The  relative  brightness  of  the  com- 
mon  sources  of  light  are  approximately  as  follows  ' :  — 

Sunlight  at  the  sun's  surface loo.ooo  candle  power. 

Most  powei  'ul  electric  arc 55,000       "         '« 

Most  powerful  calcium  light I'soo       »         <« 

Light  of  ordinary  gas-burin  r 12  to  10       '•         «« 

Standard  candle ,       ,,         „ 

''The  total  quantity  of  light  emitted  by  the  sun  is  equivalent 
to  the  light  of  6,300,000,000,000,000,000,000,000,000  (six  thou- 
sand three  hundred  bUlions  of  billions)  candles."    Of  this  enor- 

-J .J  _.  "s-J!-  viiv  caiiu  mtciuupts  oD  extremeiv  small 

fraction. 

'  0.  ▲.  Young. 


ii 


332 


RADIANT  ENERGY.  —  LIGHT. 
QUESTIONS. 


1-    Suppose  that  a  ligiitod  candle  );;  niamfi  j,,  fi,„  „„  , 
three  cubical  roo:ns  re^ectlvely  10.  2       X^t^.^T'"^      '"'^  ^^ 
siugJewall  Of  the  first  roo.,  rL  v    ;n    ^or  iLl";    '  "'T'' " 

wall  of  either  of  the  other  rooms?  ^^*  *'""  *  ''"^'^« 

;.st  .0. .  rf  no.  What  ^r.j:z:^  ^:i:^:jt^.^ 

of '^he^i:.!;^' i'lT"?'^'"'  '''""  fromacandle  flame,  the  area 
Indl  w  M  "'*'■'*  "'^'^  ''^  **  s^'-^e"  75e™  distant  from  the 

candle  wu.  ,':  .,o^v  many  times  the  area  of  the  boar.?  Then  t™i^hl 
nterceptod  ,  the  bo«rdwill  illuminate  how  much  of  the  surface  of 
the  scicen  i^  the  board  is  withdrawn? 

4.    Give  a  reason  for  the  law  of  Inverse  Squares. 

6.   To  wnat  besides  light  has  this  law  been  found  applicable? 

6.   The  tvvo  sides  of  a  paper  disk  are  iUumiuated  equally  by  a  candle 
«ume  50-  distantonone  side  and  agas  flame  200cn.  distant  on  the  o^^ 

theiJsrcr  '''  ''^*^""^"  "'"^^  *"^  ^^^^*^  ^'  ^^-'  ^'«^--  from 


Fig.  241. 


LII.     VISUAL   ANGLE,  ETC. 

r.«rH^^^"     ^^^^^1    angle.  -  Experiment.     Prick  a  oi„-hole  in  a 
card  place  an  eye  near  the  hole,  and  look  at  a  pin  ab.   .    =0^  dista"it 
Then  bnng  the  pin  slowly  toward  the  eye.     What  do  j  serve? 


Why  IS  this  ?     v-e  see  an  object  by  mean, 
on  the  retina  of    -  eye,  and  itP,  apparent 
mined  by  the  extent  of  the  retina  covered  b. 


^  fTaage  formed 

lUuie  is  deter- 

'oiage.     Rays 


METHOD  OF   ESTIMATING   SIZE. 


333 


proceeding  from  opposite  extremities  of  an  object,  as  AB,  Fig- 
ure 241,  meet  and  cross  one  anotlier  in  the  window  of  tlie  eye, 
usually  called  the  p?ipi7.  Now,  as  the  distance  between  the 
points  of  the  blades  of  a  pair  of  scissors  depends  upon  the 
angle  that  the  handles  form  with  one  another,  so  the  size  of  the 
image  formed  on  the  retina  depends  upon  the  size  of  the  angle, 
called  the  visual  angle,  formed  by  these  rays  as  they  enter  the 
eye.  But  the  size  of  the  visual  angle  diminishes  as  the  distance 
of  the  object  from  the  eye  increases,  as  shown  in  the  diagram ; 
e.g.,  at  twice  the  distance  the  angle  is  one-half  as  great,  at 
three  times  the  distance  the  angle  is  one-third  as  great,  and  so 
on.  Hence,  the  apparent  size  of  an  object  diminishes  as  its  dis- 
tancefrom  the  eye  increases. 


QUESTIONS. 

1.  Why  do  the  rails  of  a  railroad  track  appear  to  converge  as  their 
distance  from  the  observer  increases? 

2.  Why,  in  looking  through  a  long  hall  or  tunnel,  do  the  floor  and 
the  ceiling  appear  to  approach  one  another? 

8.  Why  do  parallel  lines,  retreating  from  the  eye,  appear  to  converge? 
4.  Why  can  a  book,  held  in  front  of  the  face,  entkely  conceal  from 
view  a  house? 


§  286.  Methods  of  estimating  size.  ~  Let  a  man  stand  beside 
a  boy  of  half  his  hight,  and  to  an  observer,  twenty  feet  distant,  the  for- 
mer will  subtend  a  visual  angle  twice  as  great  as  the  latter,  and  will 
appear  twice  as  tall.  Then,  let  the  man  move  back  twenty  feet  farther 
from  the  observer,  and  he  and  the  boy  will  then  subtend  equal  angles, 
but  they  will  not  appear  to  be  of  equal  hight,  nor  will  the  man's  hight 
appear  diminished  in  a  very  perceptible  degree.  The  sun  and  the  moon 
are  about  4,000  miles  nearer  to  us  when  they  are  in  the  zenith  than  when 
near  the  horizon,  but  in  the  latter  case  they  appear  much  larger. 
It  makes  a  great  difference  in  the  variation  of  the  apparent  size  of  a 
pin,  as  it  moved  to  and  from  the  eye,  whether  it  is  seen  through  a 
pin-hole  in  a  card  or  whether  the  card  is  removed ;  and,  again,  whether 
it  is  seen  with  one  eye  or  both  eyes.  Tlie  fact  is,  that  In  estimating 
tbe  s\w  of  objects,  our  judjjment  is  influenced  by  many  other  things 


884 


BADIANT   KNKHGy.  — uoHT. 


besides  the  visual  angles  which  they  subten^l     n      , 
real  size  of  au  object,  also  of  the  fact  th«  ttt  i     7  ^"««^>«^g«  ^^  the 
n  distance  is  to  ,Ii„,„ish  the  apparent  .eo   /^nr'"  "'  '"^  '"^^^««« 
ect  does  not  bccono  shorter  .'^  it  rit      al" ',f/' '^"^  "'«»  an  ob- 
toward  correctin-'  an  estin.ate  based  on  tho«t      T  "''  ^^^«  '""^h 
Our  estimate  of  the  size  of  obje  L  whdo  «  ?,      "',''  '*'"^'  ^"^'«- 
enced  n.uch  by  comparison  witi  obje^  «!«  t  .1     ,"?'°"^"  ^^  ^°«"- 
islcnown.as  in  tlie  case  of  the  sun  an  f  /  '''""'^^  whose  size 

nmge  with  other  objects  in  the  I,o,..7  /""""  '^''*'"  ^^^y  are  in 

Whether  it  is  seen  alone  throu.  1,  a  Ik  ,;"'  ?  '"  "''  ^'^««  «^  ^^^^  P^"- 
objects.  Again,  when  we  lo^k  at  "  7,  "l  •''^"J""^tion  with  other 
obliged  to  turn  the  eyes  in  ^  ,  "■'"''^  ^'^''  ''"^h  ^yes  we  are 

upproachesorrecedes.ro  rLr;i.r^:''''\r''^'''''"''^^  -  -  object 
to  enter  the  eye.  The  effort  nec^  "^  .y  t  a.,:";  T  "''^ff  ""^'^  ^^""°- 
so  as  to  see  objects  at  different  cHsta.lr  ?'  i  ^"''"°"  °^  ^^^  ^y««. 
estimate  of  their  size.     Hen  e     1  e  L      ''^  '"  ^''''"''"^'  ^  ^«"««t 

appear  to  undergo  so  grea  a    hiu^eir,^^^^^^^^^       '"^'^  ^>'^«  ^«-  -* 
the  observer,  as  when  seen  by  one  eye     We  I     T''  *"  "^"^  '^^'^ 
scions  of  going  througl,  ll.e  processe„  o7t         f''*  '**  *^^  "™«  «o°- 
because  it  has  becom^  a  matter  0^1  ,/!;«''•'"*  """^'«*^^  «bo^«. 
readily  make  these  allowances  ^he/vTw, ,!!.":;     f"'''^'  "^  "°^« 
direction  than  in  a  vertical  direction,  t^m^lt^T    ""  ^  ^^^'^-"^-^ 
man  seen  at  a  considerable  hight  lool^s  small  ..f  *       '''"  P"*^*'"*'-     ^ 
equal  distance  in  a  horizontal  lec«o„S;     '''''''"  '"'''  ^'  ^^ 
m.on  near  the  horizon  may,  perhapt "e  e^^Tr  ^'  *'^  ^^^^^ 
man  born  blind  suddenly  acquires  tL  power  of     1  j  ,  "'^^  T^'     "  * 
ludicrous  mistalies  in  judging  of  si/e  «,ui  n  ^'  ^"^  ''*  '*''*'*  '"akes 

hohas  not  acquired  thL  meS:. ,:       "^,^^    ;^^^^^^^^^  because 

out  its  hands  to  seize  a  bird  that  ^^^^.^  XZ:^^'' 

so  groat  that  no  ordinary  ^eansTn  m^ll^lV''''  !^ 
so  short.     But  the  distances  of  the  iZvZThll  '  ''  '' 

-t.t.e  that  their  Ii,htre.nire;r^ 

To    illustrate    nnp    mofhr^H      !a*     T      •        -n- 

"trfklng a  sl„gK,srr;kT;veryl ?„;■'",!'''''•?  ^12  „pre,e„,  a  clock 

w.c„  a  pe.„„  w .... ,  r  °:«r,;':;:s;.f  ;.:er  rr 


VELOCITY    OF    LIGHT. 


335 


ledge  of  the 
an  increase 
that  an  ob- 
does  much 
sual  angle, 
vn  is  influ- 
whose  size 
hey  are  in 
of  the  pin, 
with  other 
'^es  we  are 

an  object 
y  continue 
f  the  eyes, 

a  correct 

does  not 
and  from 
time  con- 
id  above, 

we  more 
orizontal 
ctice.  A 
en  at  an 
the  large 
ay-  If  a 
St  makes 

because 
ill  reach 
ve. 


t  light- 
peed  is 
e,  it  is 
o  great 
)  easily 


1  clock 
around 
is  four 


miles  So  long  as  W  remains  at  E,  the  strokes  come  exactly  once  an 
hour  by  his  watch;  but  as  lie  moves  away,  the  intervals  become  slightly 
longer,  so  that,  however  long  he  is  on  the  road,  if  the  watch  and  c'ock 
run  accurately,  when  he  has  reached  E'  the  sound  of  the  bell  reaches 
mn  about  twenty  seconds  after  the  hour.  As  he  continues  back  to  E 
the  sounds  come  more  and  more  nearly  on  time,  so  that  at  E  they  are 
just  at  the  proper  time.     Similarly,  at  regular  intervals  in  the  heavens 

an  eclipse  of  ono 
of  Jupiter's  moons 
takes    place ;    the 
average      interval 
being  known,  add 
it  to  the  time  at 
which  an    eclipse 
is  observed  when 
the  earth  is   hmr 
E,  and  thus  we  may 
predict  the  times 
of  an  eclipse  for 
years  ahead.     All 
the    eclipses,    ex- 
cept    when      the 
earth  is  at  E,  are 
observed  to  be  a 
little    behind     the 
predicted  times ;  at 
.     ^  E'  as  much  as  ICi 

minutes.     But  at  E'  the  light  has  had  to   travel  184,000,000  miles 
farther  to  reach  the  eye  than  at  E. 

Hence,  light  must  travel  at  the  rate  of  184,000,000 -5-(lG^  x  60) 
=  about  186,000  miles  (about  300,000'^'")  in  a  second. 

Sound  creeps  along  at  the  comparatively  slow  pace  of  about 
one-fifth  of  a  mile  (or  i^"^)  per  second.  The  former  is  tiie  ve- 
locity wHi-  which  waves  in  ether  arc  transmitted  ;  the  latter,  the 
veloci^)  V  ith  which  waves  in  air  move  forward.  This  great 
difference  can  be  accounted  for  only  on  the  supposition  that  the 
rarity  and  elasticity  of  ether  are  enormously  greater  than  that  of 
air. 


I' 


im 


nm 


liADiANT  ENERGY.  —  t 


rOHT. 


I-in.     REFLECTION   OF   LIGHT. 

AI,   Fi.M„.o  243,   is  u  .>oarrI   ...:  square     'f /"P'*"*"^   ««   follows: 
fastened  to  one  of  its  si.I.s.    e  is  a  rod  2'' .n,""^'  ^  ''''''"'  ''"'  «a"are 
c  ose  to  the  ..,c,dle  of  one  of  the  ed'es  of    he  ™V""""'  ^"  "'^  '^^-'J 
I     th  "'V"'-^^'^«  °^-  the  board.    D  F  isan  a  v  nf '"'°'''  ""^'  P^'-P-ndicu 
-  the  rod.    Tl,e  outer  edge  of  the  arc  Id       T"''^''"'""^  ^^PP^^ted 
.^'  the  length  of  the  rod,  and  Is  divided,  f  ^f'^^''^'^^^  by  a  radius  equal 
'^r,  orifice  of  the  tube  C  of  ul  L.Z  ;       "'"^  '^''^'■^««-     ^over  the  one„ 
in  its  center  by  a  elrculaS^.T^";-;?  ' -J^'^  ^  ^'-"'-  tin    ieTc.:;- 
beam  of  sunlight  mc.  '         '"  ^i'araeter,  and  admit  a  slender 

H  St::^  ,^:- -  r:;;- -  - -m  of  „,.  m.  st.. 

A  bea™  Of  light  as  it  approaches    „  obta  •  ""'?  ''  ''  ""«  P^'"*- 

The  beam,  unable  to  pass  th  ough         1  '    '  T''^  '"  '■""■^^'  '^  *^«'«- 

m.rror,  ,s  reflected  by  this  surface       i    ^       '  'V  ''''''^  '"'•'^^''-  ^^  ".0 

of  the  perpendicular  oc.     A  beam  nf  1    .  ;'''.'  ''^  *^^  opposite  sldo 

r.;fec.ec.  Z.C  .«.     The  «pot  of  ll^t         '''  "''''  ''^'^'^'^  ^^  termed  « 

on  the   arc   produced  by  the  re-  Fi;..24.r 

fleeted  beam  will  be  found  to  be 

the  same  number  of  degrees  dis- 

tanfromtheperpendiculr^-asthe 
spot   produced    by    the    incident 

the  a«^  .  0/ .,;?,  '^' 1«  '-qual  to 
the  angle  „,co,  called  the  a„^/.o/ 
tndence      i^eline  the  mirror  s^ 

that  the  incident  be.,,. ay  striK-e 
^,"'"*^'-"'°''«  or  le..  obliquely, 
f "     "'^  ^^fl'^<=ted  beam  will  leave 

Ifl  ";« /••»th  of  the  incident  . 

reflected  beam  luminous  by  int  •  ^ 

^     '  So,no  n^eans  of  introducW  ,  bo,™         '  u         '  ''''"'^  "^  "''"''"'  ^"°'"  *«"■  '' 

t"  experimenting  with  light     Th^  '  '"'"^'''  '"'°  *  '^'"•kened  room    .  In.' 

•ition  that  the  pupil  i^  iff''    ^'"'^'^Periments  on  this  subject  J^nZ  T      ''"'"•I^ensablo 

f tooting  appaS  '  uCll  t'hl    ''  """^  °'  -compiis    n^  1     £;::»"  "'!  '"^P"" 
'n  Mayer  and  I'lrnanl  .  m.?  v     P^'P"'"'  "^^aUy  called  a  bL^;      ^"^'^"'"'^  ■>^'-  con- 

'lescriptfon  of  an  Inexpensive       '''""J'"'"'^''."  Published  by  £«;  &  Shi'^l'"'"  ^  '''°-  ^"^ 
»'  the  Append!,.      '^^^"^'^^  "^P-'-  ^-i.ed  hy  the  autL^ry^etu^d'-iX^on  H 


mFFl'SEl)  LKiHT. 


337 


*8   follows : 
8<""  square 
n  the  board 
'erpendicu 
I  supported 
iilius  equal 
t*  the  open- 
tin  pierced 
t  a  sleuder 

nay  strike 
Jne  point. 
'■^  •<  beam. 
ice  of  the 
3sito  side 
termed  a 


;)<>nsablo 
i  suppo- 
'oi-  con- 
s  found 
).,  New 
on.  A 
ition  H 


paper,  and  the  angles  formed  with  the  perpendinilar  will  be  onit* 

rrcL  it:^  "^  ^'^  ''^  ^^""''  ^^-^^^-^  ^^  ^^^  ^-"  ^^- '/  ^i!^- 

of^n!?M  ,^^^^?^  "ell*-  E'^Perimentl.  Introduce  a  small  beam 
of  light  into  a  darkened  roon,  by  means  of  a  parte  lumierc  anZ'Z 
n  its  path  a  mirror.  The  light  is  reflected  in  I  definite  dir  cT  on'  If 
the  eye  is  placed  so  as  to  receive  the  reflected  light,  it  will  see  not  the 
•mrror,  but  the  image  of  ■  sun.  and  the  light  will  ^e  paillly  i  tens* 
Substitute  for  the  mirror  a  piece  of  unglazed  paper  The  ^^t 
not  reflected  by  the  paper  In  any  definite  Irectiorbut  is  s  at  r  d  1 
every  direction,  illuminating  objects  in  the  vicinity  ;„d  rendedng  hem 
visible.  Looking  at  the  paper,  you  see,  not  an  image  o,'  the  sun  b"t 
the  paper,  and  you  may  see  it  equally  well  in  all  directions 


Pig.  244. 


The  dull  surface  of  the  paper  receives  light  in  a  definite  direc- 
t        but  reflects  it  in  every  direction  ;  in  other  words,  it  scatters 
or  d^ffu.'.'s  the  light.     The  difference  in  the  phenomena  in  the 
two  cases  is  caused  by  the  difference  in  the  smoothness  of  the 
two  reflecting  surfaces.     AB,  Figure  244,  represents  a  smooth 
surface,  like  that  of  glass,  which  reflects  nearlr  all  the  rays  of 
light  m  the  same  direction,  because   nearly  ail  the  o  ints  of 
reflection  are  in  the  same  plane.     CD  represent,  .  surface  of 
paper  havmg  the  roughness  of  its  surface  greatly  exaggerated. 
Ihe  vai  u,u8  points  of  reflection  are  turned  in  every  possible  direc- 
■on  ;  consequently,  light  is  reflected  in  every  direction.     Thus, 
the  dull  surfaces  of  various  objects  around  us  reflect  light  in  all 
(Lrections,  and  are  consequently  visibV  from  every  side.    Obiects 
rendered  visible  by  reflected  light  are  sud  to  be  illuminated. 

,"-■   """" -e^-^is::-,  :-o;icctcc-.  light  wf  Mcc  Imagcs  of  obiects  in 

mirrors,  but  only  in  definite  directions;  by  means  of  diffused  ijht  we 
«ee  the  mirror  itself  in  every  direction.  Whether  we  see  the  image  of 
the  source  of  the  light  (the  eye  being  situated  so  as  to  receive  the 


IS 

it 


888 


BADIANT  ENEBGY.  ~  LIGHT. 


'%)    i 


liquids  at  rest  are  excellent^,  rors       tl  .f  "■""•     ^""^''^^  -' 

smooth  surface  of  a  pond  surroZi;,!  ,     .  ««'»«"'°e«  difficult  to  see  a 
as  th.  oyo  is  occupied  byt  "e  X  eVLr'  T  T^'"^'""^'^^  ^'^^^-' 

faint  breath  of  wind,  sligluiyrSS  '^''''  "''J^^^^-'  ^"t  « 

Kxperlment  2.  Place  aTsS^   .   '"'■^'''''  ^'"  ''^'^^^l  the  water. 

flan.e  so  that  Its  rays  na^fort/iLr       7  '  ''''^'  ^""  ""'''  «  ^-''Je 

and  notice  the  brigLnesJoflTs  1„Z  T'  ''**!!  '''  ^"^"'"  ^^''f-^. 

so  that  the  incident  and  reflected  ra?«  7  '^"  "'""^"^  '^"^  *^«  «:^« 

surface  o,  the  li<,uid.  and  ,^  L  IV'  ""Tl  ^  P"'^"^'«'  ^^=^«  ^^e 

comes.     Notice  how  much  Ster  2     ^'^  .^'^'''''  ^''^  ^'"*^«  ^«- 

ture  appear  when  viewed  verv  1.1     /"'".^'^''^  ''''^^'''  °^  ^»™'- 

rcflected  less  obliquely     Also  notlp^r^^'  '''""  ^^''^"  '^^^^  ^^  "S^t 

light  .fleeted  frol  th'e  stlZTofZ  tllZt  b"ef "  '^r""^  '^  ''^ 

waujr,  onij  IS  parts  are  reflected  •  nf  An°   oo 
reflected;  at  80",  833  parts  ;  aad  at  8  iV2" Vart^    ^7  r"" 
IS  not  even  approximate! v  tr„«  ^i'       .  ,  ^  ^''®  ^^ove 

metallic  reflec'tL,  s^h  aVgaLa,  T'  "  "'^^^"^^^  '^^^^'^^ 

Ml?4t^Te:i:L^T^i-^^^^^^^ 

gent  rays  proceeding  from  the  poSt  A  nf  u-  *  P"''""  ^'^  ^^^^r- 

Perpendlculars  at  thf  points  of  Sence    or"th?"'  ^  "^     ^"^«"« 
rays  strike  the  mirror,  and  making  th!!'    ,  P°'"*'  ""^''^  ^hese 

^,-o„,.„^    ^-, ,    ,     ^  "^  »»»n-or.      In  hke  manner  ennfitrn/.t  „ 
construct  another  diagram,  and  show  that  conv4ent 


Jls,  or  both 
;hnes8  pos- 
irfaces  are 
urfaces  of 
It  to  see  a 
by  clouds, 
cts:  but  a 
the  water. 
(1  a  candle 
1  surface, 
id  the  eye 
graze  the 
image  be- 
of  furnl- 
by  light 
ing  is  the 
sun  sets, 
ft  to  our 


ncreasss 
perpen- 
s  a  sur- 
irts  are 
e  above 
having 


■fires.— 
f  diver- 
Irectinjj 
e  these 
qua!  to 
id  rays 


after 

VVtOt.   ft 

'  ajler 
ergent 


KEFLECTIOX   FUOM   I'LANE  MlUItOKS.  339 

incident  rays  arc  convergent  after  reflection.     To  an  eye  placed 
at  C,  the  points  from  which  the  rays  appear  to  come  are  of  course 

in  the  direction  of  the  rays  as  they 
oMtor  the  eye.     These  points  may  be 
found  by  continuing  the  rays  CB  and 
C  E  behind  the  mirror,  till  they  moot 
at  the  points  D  and  N.     Every  point 
of  the  object  All  sends  out  its  peu- 
ciis   of   rays,   and   those   that  strike 
the  mirror  at  a  suitable  angle  to  be 
reflected  to  the  eye,  produce  on  the 
retina  of   the  eye   an  image  of  that 
l)oint,  and  the  point  from  which  the 
light  appears  to  emanate  is  found,  as 
previously  described.     Thus,  the  pencils  EC  and  BC  appear  to 
emanate  from  the  points  N  and  D,  and  the  whole  body  of  li-rht 
received  by  the  eye  seems  to  come  from  an  apparent  object  ND 
behind  the  mirror.     This  apparent  object  is  called  an  image, 
but  as  of  course  there  can  be  no  real  image  formed  there,  it  is 
called    a  virtual  or  ' 

an    imaginary    image.   ^^^^^ 

It  will  be  seen,  by 
construction,  that  an 
image  in  a  plane 
mirror  ajrpears  as  far 
behind  the  mirror  aa 
the  object  is  in  front  of 
it,  and  is  of  the  same 
size  and  shape  as  the 
object. 

r- ^  ^^^     Eeflection  from  concave  mirrors.  —  Let  M  M' 

iMg.  .-.o  represent  a  section  of  a  concave  mirror,  which  may 
be  regarded  as  a  small  part  of  a  hollow  spherical  shell  having  a 
pohshod  interior  surface.     The  distance  M  M'  is  called  tho  apcr^ 


1 1' 

ii'i 


1 


340 


I^AI>IANTKXEU(JV.-L,GHT. 


tH 


ture  of  the  mirror      C  ia  ti,^        j.       ^ 

straight  line  DG,  d  a [ u  til,  ^^  "'*"  "'  *"  ""-"■•  A 
the  vertex  is  c.led  ti.e Tn"  ^  f  L^fT  "  "'  '""''"'•'  -" 
mirror  may  be  eonsidered  TlT  I  ""™''-  ^  concave 
small  plane  snrfaee  Ml  ",^0 ft,""  °'  "°  '"""''»  """"er  of 
CB,  are  p.rpendieular  to  th  sm^.r™'  f?  ^^'  °<^-  -»" 
If  C  be  a  luminous  point  it  f,  !"  ,  I?™  "■'""''  ""y  strike. 
<Vom  this  point,  and  sW  J  tL?  *'■"  ""  "«'"  "'"■""■'ting 

its  source  at  C.  "^  ""  '"'*™'''  ""'  he  reflected  back  t^ 

...e^Li^:„'r::^:rx^r:srtT: ""-  -«-■ 

.hat  3trme,  the  n,l™r.    S  ITv'Sft  "if  "^^^  '■™'^"  '>"'«'■« 
and  B,  and  draw  the  JI„e»  AF  ami  BF  It-      .r'""  "'  '""'^n"*  A 

pr;;r,2hr;;;s^^^^^^^^ 

h-es  .F  and  BF  represent  theXt ttn  o^ ra^tirS  J" 

It  will  be  seen  that  the  rays  after  refle<.tr„„ 
and  meet  at  the  point  P,  called        ;:     ""ThT  """r!^™'' 

and  BE  would  repLrrtbrrer^d'^yr^d*;  ^^b^ 
the  focus  of  these  nvK      «,-„      ^i        ,     -^  '       "  ^  would  be 

points  is  sueb  that^i^  e^t:  nrC^Lrtr"  T  """^ 

'■-.»  Of  one  JfZJz:  zrz  7  "'r """  "^ 

emanating  from  E  aro  u..  I-  ^  '^^^^  ^^  and  EB 

cnanatin    ^o^  f  ^l^^  T, tTt^ntT  ""'l  "^  ''"<'^«- 
striking  the  same  points     nZ.  "™  ""^  '""">''  ""d 


id  is  called 
airror.     A 
ature  and 
^  concave 
number  of 
CG,  and 
ey  strike, 
manatinsr 
d  back  to 

.  To  find 
reflection, 
nting  two 
'1  of  light 
'idence  A 
reflection 
lines  rep- 
t>n.  The 
Jctlon. 

^ergent, 
t  is  the 

E.  It 
les  AE 
)uld  be 
ro  such 
'I'ought 

conju- 
lat  the 
Id  EB 
dFB, 
r,  and 
riking 

it  the 
'■  rays 


FORMATION  OF   IMAGES. 


341 


rays  may  be  regarded  as  practically  parallel  when  their  source 

is  at  a  very  great  distance,  e.g.,  the  sun's  rays.     If  a  sunbeam, 

consisting  of  a  bundle  of  parallel  rays,  as  E  A,  D  G,  and  H  B 

(Fig.  249),  strike  a  concave  mirror  parallel  with  its  principal 

Fig.  249.  ^^^^-i  *^ey  become  convergent  by  reflection, 

and  meet  at  a  point  (F)  in  the  principal  axis. 

This  point,  called  the  principal  focus,  is  just 

half-way  between  the  center  of  curvature  and 

the  vertex  of  the  mirror. 

On  the  other  hand,  it  is  obvious  that  diver- 
gent rays  emanating  from  the  principal  ftitus 
of  a  concave  mirror  become  parallel  by  reflection. 

If  a  small  piece  of  paper  is  placed  at  the  principal  focus  of  a 
concave  mirror,  and  the  mirror  is  exposed  to  the  parallel  rays 
of  the  sun,  the  paper  will  quickly  burn,  showing  that  the  focus 
of  light  is  also  a  focus  of  heat;  or,  in  other  words,  that  all  forms 
of  radiant  energy  follow  the  same  laws  of  reflection  as  light. 

Construct  a  diagram,  and  show  that  rays  of  light  proceed- 
ing from  a  point  between  the  principal  f,,^ds  and  the  mirror 
are  divergent  after  reflection,  but  less  divergent  than  the  inci- 
dent rays.  Reversing  the  direction  of  the  light,  the  same  dia- 
gram will  show  that  convergent  rays  of  light  are  rendered  more 
convergent  by  reflection  from  concave  mirrors.  The  general 
effect  of  a  concave  mirror  is  to  increase  the  convergence  or  to  de- 
crease the  divergence  of  incident  rays. 

The  statement,  that  parallel  rays  after  reflection  from  a  concave 
mirror  meet  at  the  principal  focus,  is  only  approximately  true.  The 
smaUer  the  aperture  of  the  mirror,  the  more  nearly  true  is  the  state- 
ment. It  is  strictly  true  only  of  parabolic  mirrors,  such  as  are  used 
with  the  head-lights  of  locomotives.  Construct  a  diagram  representing 
a  mirror  of  large  aperture,  and  it  will  be  found  that  those  rays  that 
strilie  the  mirror  at  considerable  distance  from  its  center,  intersect  the 
principal  asis  after  reflection  at  points  nearer  to  the  mirror  than  the 
principal  focus. 

§  292.  Formationofimages.  — Experiment  1.  In  a  dark  room 
bold  the  concave  side  of  a  bright  silver  dessert  spoon  a  little  distance 


ip 


I  •( 


342 


KADIANT   ENERGY. — LIGHT. 


in  front  of   the  face,  and  introduce   a  candle-flame  between  the  spoon 
and  your  eyes.     What  do  you  see?    Why?    See  §  078  "«  spoon 

Experiment  2.  Turn  the  convex  side  of  the  spoon  toward  you 
What  do  you  see?    Explaiu.  ^ 

Experiments.  Repeat  the  two  preceding  experiments,  holdin-'  the 
spoon  between  the  flame  and  the  ryes,  but  not  so  as  to  screen  tlie'lace 
from  the  light,  and  you  will  see  f  imilar  images  of  yourself 

To  determine  the  position  and  kind  of  images  formed  of  objects 
placed  in  front  of  concave  mirrors,  proceed  as  follows:  Locate  the 
object,  as  D  L,  Figure  250.  Draw  lines,  E A  and  DB,  from  the  extrem- 
ities of  the  object  through  the  center  j,j  350 
of  curvature  of  the  mirror,  to  meet  the  ' 
mirror.  These  lines  arc  called  the  sec- 
ondary axes.  Incident  rays  along  these 
lines  will  return  by  the  same  paths 
after  reflection.  (Why?)  Draw  another 
line  from  D  to  any  point  in  the  mirror, 
e.ff.,  to  F,  to  represent  any  other  of  the 

infinite  number  of  rays  emanating  from  

D  Make  the  angle  of  reflection  CFD'  equal  to  the  angle  of  in- 
cidence CFD,  and  the  reflected  ray  will  intersect  the  secondary  avis 
DB  at  the  point  D'.  This  point  is  the  conjugate  focus  of  all  ravs 
proceechng  from  D.  Consequently,  an  in.age  of  the  point  D  is  formed 
at  D'.   This  image  is  called 

a  real  image,  because  rays   ■ — ■ Fig.  251. 

actually  meet  at  this  point. 
In  a  similar  manner,  And  the 
pointE',thc  conjiigate  focus 
of  the  point  E.  The  images 
of  intermediate  points  be- 
tween D  and  E  lie  between 
the  points  D' and  E';  and, 
consequently,  the  image  of 
the  object  liesbetweenthose 

points  as  extremities.  

If,  for  the  second  ray  to  be  drawn  from  any  point    we   select 
that  ray  which  is  parallel  with  the  principal  axis,  as  AG   it  n-e  '5 
will  not  be  neeessary  to  measure  angles.     For  this  v^^^^. 
tion    must  pass  through  the  principal  n„.„s  F;  and  con  ...,uent  y    1  .■ 
conju^at.  i.cus  A'  is  easily  found,  and  so  for  the  point  B'  an     lute 


FORMATION  OF    IJIAGES. 


343 


■ei)  the  spoon 
toward  you 

f,  liolding  the 

t'eeu  the  taco 

F. 

d  of  objects 

:   Locate  the 

ti  the  extrem- 

10. 


■v  F 


mgle  of  iu- 

lODdary  axis 

of  all  rays 

D  is  formed 


we  select 
,:L,nire  251,  It 
fter  rc'll(!c- 
i|ueiitly  til." 
'  iiiul  luter- 


Fig.  252. 


mediate  points.     Both  methods  of  constructing  images  should  be  oraa 
tised  by  the  pupil.  ^ 

It  thus  appears  that  an  image  of  an  object  2')laced  beyond  thd 
center  of  curvature  of  a  concave  mirror  is  real,  inverted,  smaller 
than  the  object,  and  located  between  the  center  of  curvature  and  the 
principal  focus  of  the  mirror.    An  eye  placed  in  a  suitable  posi- 

tion  to  receive  the  light,  as  at 
II  (Fig.  252),  will  receive  the 
same  impressiou  from  the  re, 
fleeted  rays  as  if  the  image 
E'  D'  were  a  real  object.  For 
a  cone  of  rays  originally  eman- 
ates from  (say)  the  point  D  of 
the  object,  but  it  enters  the  eye 
as  if  emanating  from  D',  and  consequently  api)ears  to  originate 
from  the  latter  point.  (§  278.)  A  person  standing  in  frontof  such 
a  mirror,  at  a  distance  greater  than  its  radius  of  curvature,  will 
see  an  imago  of  himself  suspended,  as  it  were,  in  mid-air.  Or, 
if  in  a  darkened  room  an  illuminated  object  is  placed  in  front  of 
the  mirror,  ;uid  a  small  oiled-paper  screen  is  placed  where  the 
image  is  formed,  a  large  audience  may  see  the  image 'projected 
upon  the  screen. 

If  E'  D'  (Fig.  250)  is  taken  as  the  object,  then  the  direction 

pig_253,  ^^  ''"^  ^'S'lt  in  the  diagram 

will  be  reversed,  and  ED 
will  represent  the  image. 
Hence,  the  image  of  an  ob- 
ject jylaced  between  the  prin- 
cipal f)cns  and  the  center  of 
curvature  is  also  real  and 
inverted,  but  larger  than  the 
object,  and  located  beyond 
the  center  of  curvature.  T'le  image  in  this  ease  may  bo  pro- 
jected upon  a  screen,  but  it  will  not  be  so  bright  as  in  the 
former  case,  because  the  light  is  spread  over  a  larger  surface. 


I 


»44 


IlAblANT   EKERGV.  — MGHT. 


6'ii 


a 


1 


II 


Constnict  the  image  of  an  object  placed  between  the  principa. 
focus  and  the  mirror,  as  in  Figure  253.  It  will  be  seen  in  this 
case  that  a  pencil  of  rays  proceeding  from 

any  point  of  an  object,  e.g.,  D,  has  no   ^'''^' 

actual  focus,  but  appears  to  proceed  from 
a  virtual  focus  D',  back  of  the  mirror,  and 
so  with  other  points,  as  E.  The  image  of 
an  object  placed  between  the  principal  focus 
and  the  mirror  is  virtual,  erect,  larger  than 
the  object,  and  is  back  of  the  mirror. 

QUESTIONS. 

Ascertain  the  answers  to  tlie  following  questions  bv  constructing 
rrStrr^r  "*™"^  --^'^  ^-^  concluslonsTer? 

1.    When  an  object  is  located  at  a  distance  from  a  concave  miiTor 
equal  to  Its  radius,  will  any  image  be  formed?    Why? 
^2^  What  is  the  effect  of  placing  the  object  at  the  principal  focus? 

ui  t£i^? '  :)^:^n[  i^^r  '^ ' — --  --er 

Wh;n?s\tTfr:ua;?  '"'  '"^'"  '°™^^'  '' ^  concave  mirror  real?     (.) 

virLf?  /mT  -m'^'  ""  "'^  "'^''*  '"''"^^^  "^y  ^  ^«"^'«-  ""'-ror  real  or 
Inverted?  ^^  ''^"  "'  '"^"'^^  """  *^«  «'^^'-*^     C'^)  I«  "  o-ct  or 

gesS'^aslo^ttteS  o"  Si"  ^fe  dllsftiS""?  ^"^^'T*^^  -^- 
e;;.anating  from  any  point,   ^^^'^l^^:^:^  ^S'^i  ti^i 

rays?  ''  *"'  ^"''"'"'  "''''''  "'  "  '^"""^^  '"^"'^^  *«  '^^"^-t  or  to  scatter 


the  principa. 
seen  in  this 


ig.254. 


constructing 
s  by  experi- 


icave  mirror 

cipal  focus? 

•ror  smaller 

•  real?     (h) 

rror  real  or 
3  it  erect  or 


iicntly  sug- 

icil  of  rays 

a  convex 


to  scatter 


REFRACTION. 


LIV.  REFRACTION, 


345 


Experiment  1.  Across  the  bottom  of  a  rectangular  tin  basin  A  B  O 
D  Figure  255,  mark  a  scale  of  millimeterH.     lnU>  a  darkened  t!m 
admit  a  beam  of  sunlight,  so  that  its  rays  may  fall  obUque^  on  ti™ 
bottom  Of  the  ba^in,  and  note  the  place  o„  the  scale  where  th'edge  of 
Fig-  255.  the  shadow  1)  E  cast  by  the  side  of 

the  basin  1)  (J  meets  the  bottom  at  E. 
Then,  wlthouft  moving  the  basin,  fill 
it  even  full  with  water  slightly 
clouded  with  milk,  or  with  a  few 
drops  of  a  solution  of  mastic  in  alco- 
hoi.  It  will  be  found  that  the  edge 
of  the  shadow  lias  moved  from  D  E 
to  I)  F,  and  meets  the  bottom  at  F. 
Hoat  a  blackboard  rubber,  and  create 
a  cloud  oC  (lust  In  the  path  of  the 

that  the  rflv«  r  n  fKnf  .,.    ^'''''^'"  '"  *'"  '^''''  ""''  ^o"  ^^ill  discover 

that  the  rays  G  D  that  graze  the  edge  of  the  disk  at  D  become  bent 
at  the  point  where  they  enter  the  water,  and  now  move  in  the  ben 
line  GDF,  instead  of,  as  formerly,  in  the  straight  IlnTrlE     tZ  path 
of  the  light  in  the  water  is  now  nearer  to  the  vertical  side  DC 

Hrxperiment  2.  Place  a  co  n  (A    FI"   -ir.iw  «,.  m,„  k  **  i 

empty  basin,  so  that,  as  you  look  thl^S' a'l  al'h  '  in  aTard  B^C 
over  the  edge  of  the  vessel,  the  coin  is  Just  out  of  sight  Then  tiU^ 
out  movmg  the  card  or  basin.  All  the  latter  with  water  No  v^n 
lookmg  through  the  aperture  in  the  card,  the  coin  is  v  slble  T  e 
beam  of  light  AE,  which  formerly  moved  n  the  s  al4t  Hn^^^^ 
now  bent  at  E,  where  it  leaves  the  water,  and.  pJ::^^^:^^ 

aperture  in  the  card,  v.nu-rH  the  eye.  Observe 
that,  as  the  light  {.assc's  from  the  water  into 
the  air,  it  is  turned  farthi.-r  from  a  vertical  Hue 
EF;  in  other  words, /!/*«  beam  ia  farther  from 
the  vertical  than  before. 

Experiment  3.  From  the  same*  position  as 
in  the  last  cxperim(;!it,  direct  the  eye  to  the 
point  G  in  the  basitj  fl!l,:d  with  water.  Reacl» 
your  hand  around  the  basin,  and  place  your 
fluger  where  that  point  appears  to  be.  On  ex- 
amination, It  will  be  found  that  your  finger  l»  considerably  above  the 


Klg.  256. 


i; 


m 


V  ^1 

'    'fi 


346 


If 

I*; 


I:  1 


RADIANT   ENERGY.  —  LIGHT. 


Fig.  257. 


bottom  Ilonco,  the.  .feet  of  the  hcnding  of  rays  of  light,  as  they  pass 
obliquely  out  of  tcater,  is  to  cause  the  bottom  to  appear  more  elevated  than  it 
really  is;  m  other  words,  to  cause  the  water  to  appear  shallower  than  it  is 

Experiment  4.  Thrust  a  pencil  obliquely  into  water. 
What  appearance  does  it  present? 

Experiment  5.  Place  a  piece  of  wire  (Fig.  257)  verti- 
cally in  front  of  the  eye,  and  hold  a  narrow  strip  of  thick 
plate-glass  horizontally  across  the  \vire,  so  tl.ai  tlie  light 
from  the  wire  may  pass  obli<iuely  througli  the  glass  to  the 
eye.     Wliat  do  you  observe?    Why? 

produced  depends  entirely  upon  the  light  which  enters  the  eye  Hence 
Zl"n"^-r'??-'''  "^';'  '°  '°*''"  ''''  'y'  '■"  ^  ^lifferent  direction! 
sensftLn!      ''     '"''  "'  '^  '"  '"^  °"^''  '''''''''  ^'"^''-'^^  ^'>« 

When  a  beam  of  light  passes  from  one  medmm  into  another  of 
different  density,  it  is  bent  or  refracted  at  the  boundary  phxne 
between  the  two  media,  unless  it  falls  exactly  perpendieulurly 
on  this  plane.  If  it  passes  into  a  denser  medium,  it  is  refracted 
toward  a  perpendicular  to  this  plane;  if  into  a  rarer  medium,  it 
IS  refracted  from  the  perpen- 
dicular. The  angle  GDO  (Fig. 
255)  is  called  the  angle  of  inci- 
dence; FDN,  the  angle  of  re- 
fraction; and  EDF,  the  angle 
of  deviation. 


Fig.  258. 


§  293.  Cause  of  refraction. 

—  Careful  experiments  have 
proved  that  the  velocity  of  light 
is  less  in  a  dense  than  in  a  rare 
medium.  Let  the  series  of  par- 
aliel  lines  A'B  (Fig.  258)  repre-  

thll'flf  "T-'™"'"  '-""S  »  oXJeet  C,  and  passing 
through  a  rectangular  piece  of  dasa  DE,  and  ,.^...«.Lv- 

beam  of  iig„t.     Kvery  point  in  awave-ft'ont  moves";'i'tren';,aI 
vdoc,  as  long  as  it  traverses  the  same  mediun, ;  burtl^  ^ 


as  they  pass 
valed  than  it 
'T  than  it  is. 


Fig.  257. 


INDEX   OF  RKFJlA(.'TroN. 


J  sensation 
yo.  Hence, 
;  direction, 
lianges  tlie 

nother  of 
aiT  plane 
idicularly 
refracted 
edium,  it 


passing 

«-.,4.: 

th  equal 
lie  point 


847 


«  of  a  given  wave  ah  enters  the  glass  first,  and  its  velocity  is 
impeded,  while   the  point  h  retains   its   original  velocity;  so 
that,  while  the  point  a  moves  to  a',  b  moves  to  h\  and  the 
result  is   that  the  wave-front  assumes  a  new  direction  (very 
much  in  the  same  manner  as  a  line  of  soldiers  execute  a  wheel) , 
and  a  ray  or  a  line  drawn  perpendicularly  through  the  series  of 
waves  is  turned  out  of  its  original  direction  on  entering  the  glass. 
Again,  the  extremity  c  of  a  given  wave-front  cd  first  emerges 
from  the  glass,  when  its  velocity  is  immediately  quickened ;  so 
that,  while  d  advances  to  d\  c  advances  to  c',  and  the  direction 
of  the  ra}-  is  again  changed.     The  direction  of  the  ray,  after 
emerging  from  the  glass,  is  parallel  to  its  du-ection  before  enter- 
ing it,  but  it  has  suffered  a  lateral  displacement.     Let  C  repre- 
sent a  section  of  the  wire  used  in  Exp.  5,  and  the  cause  of 
the  phenomenon  observed  will  be  apparent.     If  the  beam  of 
light  strikes  the  glass  perpendicularly,  all  jioints  of  the  wave 
will  be  checked  at  the  same  instant  on  entering  the  glass  ;  con- 
sequently it  will  suffer  no  refraction. 

§294.   Index  of  refraction.  -  The  deviation  of  light,  in 
i-'ig.  259.  passing  from  one  medium  to 

another,  varies  with  the  me- 
dium and  with  tlie  angle  of 
incidence.  It  diminishes  as 
the  angle  of  incidence  dimin- 
ishes, and  is  zero  when  the 
incident  ray  is  normal  (i.e., 
l)erpendicular  to  the  surface 
of  the  medium) .  It  is  highly 
important,  knowing  the  angle 
of  incidence,  to  be  ablo  to 
determine  the  direction 
which  a  ray  of  light  will  take 
on  eutenng  a  new  medium.  Describe  a  circle  around  the  point 
of  incidence  A  (Fig.  259)  as  a  center,  with  a  radius  of  (say) 


m 


1  *  I 


tlM 


848 


RADIANT  ENEUOY.— LIGHT. 


10  ;  through  the  same  point  draw  IH  perpendicular  to  the 
surfaces  of  the  two  media,  and  to  tbi«  line  drop  perpendiculars 
BD  and  CE  from  the  points  where  the  circle  cuts  the  ray  in  the 
wo  media.  Then  suppose  that  the  perpendicular  B  D  is  A  of 
the  radms  AB;  now  this  fraction  ^  i«  called  (in  Trigonom- 
etry) the  s^ne  of  the  angle  DAB.  Hence,  «  is  the  TeZ' 
^e  angle  of  incidence.  Again,  .f  we  «upp<«e7hat  he  ^e^ot 
dicular  CE  is  p  of  the  radius,  then  the  fraction  ,V  is  1^^. 
smeof  the  angle  of  refraction.     The  .incs  of  the  two  angles 

7L%^ir''^V".Hf''  ''"^"'^-     '^'^^  ^-«-*  (-  this 
case  t)  obtmned  by  dividing  the  sine  of  the  angle  of  incidence 

by  the  sine  of  the  angle  of  refraction  i«  called  Uie  index  ofrefrac 
Uon.  It  can  be  proved  to  be  the  raiio  of  the  velocity  of  the 
incident  to  that  of  the  refracted  light.  U  is  found  that,  /or  the 
same  media  the  index  of  refraction  in  a  constant  quantity;  i.e., 
the  ;°«'^^«^t  ray  might  be  more  or  \mu  oblique,  still  this  quo 
tient  would  be  the  same.  ^ 

lii^n *  n^'''"''^'.  °^  refraction.  ~  The  Index  of  refraction  for 
hght  m  passing  from  air  into  water  te  approximately  |,  and 
from  air  into  g^ass  f  ;  and,  of  course,  if  the  order  is  reversed,  the 
reciprocal  of  these  fractions  must  be  taken  as  the  indices ;  7 
from  water  mto  air  the  index  is  f ,  from  glass  into  air  |.  When 
a  ray  passes  from  a  vacuum  into  a  medium,  the  refraclivc  index 
IS  greater  than  unity,  and  is  called  the  ahmlute  index  of  refrac 

T'fl  n  T"  ?f '''  '-^  ''^''^'''^^  ^'""^  ^^y  ^-^^-^^  ^into 
another  B,  zs  found  by  dividing  tlie  ubmlute  index  of  B  by  the 
absolute  index  of  A.  ./         j  <■  ^ 

The  refractive  index  varies  with  the  .vior  of  the  light.     (See 
W  357.)    The  following  table  U  i,.t«,„led  to  represent  il 

TABLK  OF  ABSOLUTE  WmCKS. 


Air  ui  0'  C.  and  760""»  preesure  .  1.000294 

Pure  water jjg 

Alcohol J  3» 

Spirits  of  turpentine 1.4$ 

Humors  of  the  eye  (about)     .    .  1.35 


C»rbon  Mmt]phMe j  941 

Crown  KiMMt  (a\mat)  ....!.  1  53 

i'ilai  gUm  (thont) ]  j'gj 

DJanwnd  (iibout) .'    .'  2.6 

Lca4  cbroowUi  ........  3,97 


lar  to  the 
'endiculars 
ray  in  the 
D  is  3%  of 
rrigonom- 
le  sine  of' 
10  iJerpcn- 
j%  is  the 
wo  angles 
it  (in  this 
incidence 
ofrefrac- 
•ity  of  the 
it,  for  the 
tity;  i.e., 
this  quo- 


action  for 

ly  I,  and 
srsed,  the 
)es ;  e.g., 
.  When 
ive  index 
>/  refrac- 
m  A  into 
B  by  the 

it.     (See 
mt  mean 


1.641 

1.63 

1.61 

2.5 

2.07 


ISiXERCISES. 


EXERCISES. 


849 


1.  Draw  a  straight  line  to  represent  a  surface  of  flint  glass,  and 
draw  another  line  meeting  this  obliquely  to  represent  a  ray  of  light 
passing  from  a  vacuum  into  this  medium.  Find  the  direction  of  the 
ray  after  it  enters  the  medium,  employing  the  index  as  given  in  the 
above  table. 

2.  (a)  Determine  the  index  of  refraction  for  light  in  passing  from 
water  mto  diamond,     (ft)  In  passing  from  water  into  air. 

3.  Ascertain  the  index  of  refraction  for  water  in  Exp.  1,  p.  3o0,  in 

which  sine  I  (sine  of  angle  of  incidence)  =  |g  (Fig.  255),  and  sine 

R  (sine  of  angle  of  refraction)  =  |^ .     Hence,  Uie  index  of  refraction 
_  sine_I^^E_C  ^FC  *  "" 

sine  li     El)     fd' 


350 


RADIANT   ENEROV.  —  ur.HT. 


LV.     PRISMS   AND    LENSES. 
§296.    Optical  prisms. -An   optical   prism   is   usually  a 
transparent    wedge-shaped    body.      Figure    262    represents   a 
transverse    section    of   such    a 
prism.     Let  AB  be   a  ray  of 
light  incident  upon  one  of  its 
surfaces.       On     entering     the 
prism  it  is  refracted  toward  the 
normal,  and  takes  the  direction 
BC.      On   emerging   from  the 
prism,  it  is  again  refracted,  but 

now  from  tlie  normal  in  the  direction  C  D.     The  obleet  that 
enuts  the  ray  will  appear  to  be  at  F.     Observe  that  the  ^y  A  B 
at  both  .tractions,  is  bent  toward  the  thicker  part,  or  hL,  of 

§  2SV.  Lenses. -Any  transparent  medium  bounded  by  two 
curved  .tufaces,  or  one  phmo  and  the  other  curved,  is  a  lens. 

tha^Ttl"'"",*  '•  ?°'"'''  ''  '^"P'"  ""^  ^^"«^«  ""^'^^r  •"  the  middle 
than  at  the  edge;  strong  spectacle  glasses,  or  the  large  lenses  in  an 
opera  glass,  will  answer.    Hold  one  of  the  lenses  in  the  sun's  rays  and 

two  hi  i^h^'^Vnf  ''r?  '"^  ''"'*^  ""''  ^^"''^  ^«  ''y  '"'-'^'^^  together 
two  blackboard  rubbers)  after  it  passes  through  the  leus;  also,  that  on 

a  paper  screen  all  the  rays  may  be  brought  to  a  small  circle,  or  even  a 

point,  not  far  from 

the  lens.  This  point  ^«-'^'"- 

is   called  the  fortis, 

and  its  distance  from 

the    lens,   the  focal 

length  of  the  lens. 

Find     the    focal  ___^^,^^^^ 

YoTflnd'th'l'V'"^'"*^  f  the  second,  and  then  of  the  two  together. 

th^-i-  J  "L  *''''*  ^^f  "*''•«  P^^^'-f"!  a  lens  or  combination   of 

Taraildrs  trarer;ir'  T^*'' '  *^^*  '«'  *^«  ^^-e  quickly  are' the 
para^el  rays  that  enter  different  parts  of  the  lens  brought  to  cross  ono 


EFFECT   OF   LENSES. 


85J 


usually  a 
^presents   a 


)lije(it  that 
10  ray  A  B, 
)r  base,  of 


led  by  two 
5  a  Ions, 

the  middle 
inses  in  au 
s  rays,  and 
ig  together 
Iso,  that  on 
,  or  even  a 


» together. 
1  of  either 
nation  of 
ly  are  the 

CrOSB  OQQ 


Experiment  2.  Trocuro  a  lens  thinner  in  the  middle  than  at  its 
edge.  One  of  the  small  lenses  or  eye-glasses  of  an  opera  glass  will 
answer.  Repeat  the  above  experiment  with  this  lens,  and  notice  that 
the  light  emerging  from  the  lens,  instead  ming  to  a  point,  becomes 

spread  out. 

Lenses  are  of  two  classes,  converging  and  diverging,  accord- 
ing as  they  coll(H't  or  scatter  beuuis  of  light.  Eadi  class  com- 
prises three  kinds  (Fig.  203)  :  — 


Class  I. 


1.  Double-convex 

2.  Plano-convex 

3.  Concjivo -convex 

(or  mcniscuB) 


Converging  or  curivex 
lenses,  thicker  in 
the  middle  than  at 
the  edges. 


Class  n. 
4  Double-eoncavo      i  ^''•"'Sing.    or     con. 
5.  I'lano-coneave       J      '="'''  ''■"'^■«'  ''"°"«'" 

C.  Convexo-concave   |      '"  '^^  ""'^'*'"  *'"> 
L     at  the  edges. 


A  straight  line,  as  AB,  normal  to  both  surfaces  of  a  lens, 
and  passing  througii  its  center  of  curvature,  is  called  its  pnnci- 
pal  axis.  In  every  lens  there  is  a  point  in  tlie  principal  axis 
called  the  optical  center.  Every  ray  of  light  that  passes  through 
it  has  parallel  directions  at  incidence  and  emergence,  i.e.,  can 
suffer  at  most  only  a  slight  lateral  displacement.  In  lenses  1 
and  4  it  is  half-way  between  their  respective  curved  surfaces. 
A  ray,  drawn  through  the  optical  center  from  any  point  of  an 
«)l)ject,  us  A  a  (Fig.  209),  is  called  the  secondary  axis  of  this 
point. 

§  298.   EflFect  of  lenses.— "We  may,  for  convenience  of  illus- 
Fig.264.  tration,  regard  a  convex  lens  as  composed, 

approximately,  of  two  prisms  placed  base  to 
base,  as  A  (Fig.  2G4),  and  a  concave  lens 
as  composed  of  two  prisms  with  their  edges 
in  contact,  as  B.  Inasmuch  as  a  berm  or 
pencil  of  light  ordinaril}-  strikes  a  lens  in 
such  a  manner  that  the  rays  will  be  bent 
toward  the  thicker  parts  or  baaes  of  these 
approximate  prisms,  it  is  obvious  that  the  lens  A  would  tend 
to  bend  the  transmitted  rays  toward  one  another,  while  the 
lens  B  would  tend  to  separate  them.     Tfte  general  eJJTect  of  all 


^ 


IMAGE  EVALUATION 
TEST  TARGET  (MT-S) 


1.0 


I.I 


11.25 


If  i^  IIIM 

"    lis    12.2 


us     iija 


2.0 


U   III!  1.6 


6" 


PnotDgTdphic 

Sciences 
Corporation 


33  WEST  MAIN  STREET 

WEBSTER,  NY.  14580 

(716)  872-4503 


/ 


o 


^ 


"^'1%^  ^i\\  "^"^ 


352 


RADL4.NT  ENERGY LIGHT. 


'I'M 


ft  '•- 


Vb  I 


convex  lenses  is  to  converge  transmitted  rays;  and  of  concave 
lenses,  to  cause  them  to  diverge.  Incident  rays  parallel  with  the 
principal  axis  of  a  convex  lens  are  brought  to  a  focus  F  (Fig.  265) 
at  a  point  in  the  principal  .-^xis.  This  point  is  called  the  priyi- 
cipal  focus,  i.e.,  it  is  the  focus  of  incident  rays  parallel  with  the 
principal  axis.     It  may 

be  found  by  holding  the  "^'  ^- 

lens  so  that  the  rays  of 
the  sun  may  fall  perpen- 
dicularly uiKjn  it,  and  then 
moving  a  sheet  of  jjaper 
back  and  forth  behind  it 

until   the   image   of  the _^^ 

sun  formed  on  the  paper  is  brightest  and  smallest.  Or  in  a  room 
It  may  be  found  approximately  by  holding  a  lens  at  a  considerable 
distance  from  a  window  (why  at  a  considerable  distance?),  and 
regulatmg  the  distance  of  the  paper  so  that  a  distinct  ima-e  of 
the  wmdow  will  be  projected  upon  it.  The  focal  length  il  the 
distance  of  the  optical  center  of  the  lens  to  the  center  of  the 
image  on  the  paper.  The  shorter  this  distance  the  greater  is 
the  power  of  the  lens. 

If  the   paper  is   kept  at  the  principal   focu^   for  a  short 
time   it   will  take 
fire.     Hence,  this 
is    the    focus    of 
heat  as  well  as  of 
light.     The  reason 
is    apparent    why 
convex  lenses  are 
sometimes    called 
"burning  glasses." 
A  pencil   of   rays 

^ITJ"'™  ""'  "t?"'^  "^"^  ^  (^'«-  2««).  "s  «  luminous 
pomt,  becomes  paraUel  on  emerging  from  a  convex  lens.     If 

egress,  bnf  f..  Avergence  is  loss  than  before ;  it  from  a  point 


J^ 


IMAG"ES  FORMED. 


353 


of  concave 
lei  with  the 
(Fig.2G5) 
I  the  prin- 
el  with  the 


'  in  a  room 
nsiderable 
ice?),  and 
t  image  of 
gth  is  the 
ter  of  the 
greater  is 

'  a  short 


luminous 

lens.     If 

rge  after 

a  point 


beyona  the  pnncipal  focus,  the  rays  are  rendered  convergc-t 
A  concave  lens  causes  parallel  incident  rays  to  diverge  as^'if 
they  came  from  a  point,  as  F  (Fig.  26G).     This  point  is  there- 
fore Its  principal  focus.     ~ 


point  „ 
It  is,  of  course,  a  virtual  focus. 


§299.    Conjugrate  foci. -When  a  luminous  point  S  (Fig. 
^?»i267-  267)    send.s 

rays  to  a  con- 
vex lens,  the 
emergent  rays 
converge  to 
another  point 
S';  rays  sent 
from  S'  to  the 

lens  would  converge  to  S.  Two  points  thus  related  are  called 
conjugate  foci.  The  fact,  that  rays  which  emanate  fron-  one 
point  are  caused  by  convex  lenses  to  collect  at  one  point, 
gives  rise  to  real  images,  as  in  the  case  of  concave  mirrors. 

§  300.  Images  formed.  —  Fairly  distinct  images  of  objects 
may  be  formed  through  ve^^  small  apertures  (page  327)  ;  but 
owing  to  the  sraal'  amount  of  light  that  passes  through  the 
aperture,  the  images  are  very  deficient  in  brilliancy.  If  the 
aperture  is  enlarged,  brilliancy  is  increased  at  the  expense  of 
distinctness.  (Why  ?)  A  convex  lens  enables  us  to  obtain  both 
brilliancy  and  distinctness  at  the  same  time. 

Experiment  1.  By  means  of  aporte  lumiere  A  (Fig.  268")  introduce  a 
Imrizontal  beam  of  light  into  a  darkened  room.  In  its  path  place  some 
object,  as  B,  pa.nted  In  tran  parent  colors  or  photographed  on  glass 

T,  ITT.  P^*^^*'""^' )     ««J'°"^'  t"'^  object  place  a  convex  lens  L, 

bpl  nH  1       ,  T  ^  '"■'^■"  ^-    '^^'^  '"'^'''  ^^*"^  Illuminated  bv  the 
beam  of  light,  all  the  rays  diverging  from  any  point  a  are  bent  by  the 

lens  so  as  to  come  together  at  the  point «'.    In  like  manner,  all  the  rays 

proceeding  from  c  are  brought  to  the  same  point  c' ;  and  so  also  for  aU 

intermediate  polntp.    Thus,  out  of  the  billions  of  rays  emanating  from 


354 


RADIANT  ENERGY.  —  LKIHT. 


each  of  the  millions  of  points  on  the  object,  those  that  reach  the  iens 
are  guided  by  it,  each  to  its  ovvu  appropriate  point  in  the  image  It 
IS  evident  that  there  must  result  an  image,  both  bright  and  distinct 
provided  the  screen  is  suitably  placed,  i.e.,  at  the  place  where  the 
rays  meet.  But  if  the  screen  is  p'.,ced  at  S'  or  S",  it  is  evident 
that  a  blurred  ima^e  will  be  formed.  In.stead  of  moving  the  screen 
back  and  forth,  in  order  to  "focus"  the  rays  properly,  it  is  cus- 
tomary to  move  the  lens. 

Experiment  2.  Fill  some  globular-shaped  glass  vessel  {c.,j.,  a  flask- 
decanter,  or  flsh-aquaiium)  with  water,  and  place  it  1'"  In  front  of  a 
white  wall  of  a  darkened  room.  A  little  beyond  the  vessel  place  a 
candle  flame,  and  move  it  back  and  f^rth  till  a  distinct  image  of  the 
flame  is  projected  upon  the  wall  by  the  water  lens.  Move  the  vessel 
farther  from  the  wall,  and,  on  again  focusing  the  flame,  its  image  will 
be  larger  than  before.    Repeat  the  same  with  a  glass  leus 


Fig.  268. 


By  properly  varying  the  distances  of  the  lens  and  flame  from 
the  wall,  m  the  last  experiment,  you  may  learn  that  whei  the 
distance  of  the  object  is  twice  that  of  the  princii)al  focus,  the 
object  and  image  are  of  equal  size.  When  the  ima-e  is  within 
twice  the  focal  distance  it  is  less,  and  when  beyoii.T  tliis  same 
distance  it  is  greater,  than  the  object.  In  all  cases  the  corre- 
sponding linear  dimensions  of  an  object  and  its  image  are  to  one 
another  directly  as  their  respective  distances  from  the  optical  center. 

§  301.  To  construct  the  image  formed  by 


—  Given  the  lens  L  (Fig.  269),  whose 


a  convex  lens, 
principal  focus  is  at  F  (or  F', 


reach  the  iens 
1  tlie  image.  It 
ht  and  distinct, 
lace  whore  the 
,  it  is  evident 
■ing  the  screen 
!rly,    it  is  cus- 

Gl  (r.fj.,  a  flask, 
"  In  front  of  a 
vessel  place  a 
t  image  of  the 
ove  the  vessel 
,  its  image  will 

)S. 


li  flame  f.'roni 
lat  whe:.i  the 

il  focus,  thi' 
i,t?e  is  witliiii 
(1  this  same 
es  the  corre- 
fe  are  to  one 
Dtical  center^ 

>nvex  lens. 
at  F  (or  F>, 


VTRTtTAL    IMAGES. 


S55 


for  ray    cou.mg  from  the  other  direction),  and  object  A  B  in  front  of 

t    any  two  ,)f  the  many  rays  from  A  will  determine  where  its  image  a 

formed     The  only  t.vo  M.at  can  be  traced  easily  are.  the  one  alon^^ 

the  secondary  axis  AO..  and  the  one  parallel  to  the  principal  axis  A  A^ 


Fig.  269. 


•  nd  V  MfTo"       T^T"'^  ""  "'  *"  ""'''  "''•^"S'^  *h«  Prl'^^'Pal  focus  F, 
Is     1  r    "f;.*^'  ^^'';''";"^^"''«^'^t  the  principal  axis  at  s6me  point  a ;  so  this 

oin     a      rS'e'ar""'-'   ".f.  ^'  '^^"""'^  '''  ^'  ^"^  ""  -temcdiate 
ponits  along  the  arrow.    Tlius,  a  real,  inverted  image  is  formed  at  ab. 


Fig.  270. 


§  302.  Virtual  images.  -  Since  rays  that  emanate  from  a 
pmnt  nearer  tlie  lens  than  the  principal  focus  diverge  after 
^^grcss.  It  IS  evicIeuL  that  their  focus  must  be  virtual  and  on  the 
same  side  of  the  leas  as  the  object.    Hence,  the  image  of  an 


i — 


i  I 


m 


fiADIANT  ENERGY.  —  LIGHT. 


object  placed  nearer  the  lens  than  the  principal  foms  is  virtual, 
magnified,  and  erect,  as  shown  in  Fig.  270.  A  convex  lens 
used  in  this  manner  is  called  a  simple  microscope. 

Since  the  effect  of  concave  lenses  is  to  scatter  transmitted 
rays,  pencils  of  rays  emitted  from  A  and  B  (Fig.  271),  after 

Fig.  271. 


refract!'  .liverge  as  if  they  came  from  A' and  B',  and  the 
image  will  appear  to  be  at  A'  B'.  Hence,  images  formed  by 
concave  lenses  are  virtual,  erect,  and  smaller  than  the  object. 


LVI.     PRISMATIC  ANALYSIS   OF  LIGHT.  —  SPE'^TRA. 

§  303.     Analysis  of  white  light.  —  Experiment  i.    Paste  tin- 
foil smoothly  over  one  side  of  a  glass  plate  about  5<""  square.     In  the 
center  of  the  foil  cut  a  slit  S^-"  long  by  imm  ^ide,  leaving  smooth  and 
parallel  edges.     Place  the  plate  with  the  slit  in  the  aperture  of  a 
parte  lumiire  so  as  to  exclude  all  light  from  a  darkened  room  except 
that  which  passes  through  the  slit.     Near  the  slit  interpose  a  double 
convex  lens  of  (say)    10-inch  focus.     A  narrow  sheet  of  light  will 
traverse  the  room,  and  produce  an  image,  A  B,  of  the  slit  on  a  white 
screen  placed  in  its  path.     Now  place  a  glass  prism,  C,  in  the  path  of 
the  beam  with  its  axis  (the  straight  line  connecting  the  centers  of  the 
triangular  faces)  parallel  to  A  B.     (1)  The  light  now  is  not  only  turned 
from  its  former  path,  but  that  which  before  was  a  narrow  sheet  is, 
after  emerging  from  the  prism,  spread  out  fan-like  into  a  wedge-shaped 
body,  with  its  thickest  part  restmg  on  the  screen.     (2)  The  image,  be- 
fore only  a  narrow  vertical  band,  is  now  drawn  out  into  i  long  horizontal 
ribbon  of  Ught,  D  E.   (8)  The  image,  before  white,  now  contains  aU  the 


PRISMATIC    ANALYSIS   OP  LIGHT. 


357 


» is  virtual, 
onvex   lens 

transmitted 
271),  after 


J',  and  the 

formed  by 
object. 


'"TRA. 

Paste  tin- 
ire.  In  the 
iraooth  and 
erture  of  a 
Jom  except 
ie  a  double 

light  will 
on  a  white 
the  path  of 
iters  of  the 
Jnly  turned 
w  sheet  is, 
dge-shaped 
image,  be- 
:  horizontal 
alns  all  the 


colors  of  the  rainbow,  from  red  at  one  end  to  violet  at  the  other  •  1 
passes  gradually  througli  all  the  gradations  of  orange,  yeUow,  groon, 
blue,  and  violet.     (Tlie  diftference  in  deviation  l)et\veen  the  red  and  the 
violet  is  purposely  much  exaggerated  in  the  figure.) 

Fig.  272. 


From  this  experiment  we  learn    (1)  that  white  light  is  not 
simple  in  its  composition,  but  the  result  of  a  mixture.     (2)  The 
colors  of  which  white  light  is  composed  may  be  separated  by  re- 
fraction.    (3)    The  cause  of  the  separation  is  due  to  the  different 
degrees  of  deviation  which  they  undergo  by  refraction.     Red, 
which  is  always  least  turned  aside  from  a  straight  path,  is  the 
least  refrangible  color.     Then  follow   orange,  yellow,  green, 
blue  and  violet  in  the  order  of  their  refrangibility.     The  many- 
colored  ribbon  of  light,  B  E,  is  called  tlie  solar  spectrum.  This 
separation  of  white  light  into  its  constituents  is  called  dispersion. 
The  number  of  colors  of  which  white  light  is  composed  is  really 
infinite,  but  we  have  names  for  only  seven  '^f  them;  viz.,  red 
orange,  yellow,  green,  cyan-blue,  ultramaHne-blue,  and  violet] 
and  these  are  called  the  primary  or  prismatic  colors.    The  names 


858 


RADIANT  ENERGY. — LIOHT. 


of  the  blues  are  derived  from  the  names  of  the  pigments  which 
most  closely  resemble  them.  The  rainbow  is  an  illustration  of 
a  solar  spectrum  on  a  grand  scale.  It  is  the  result  of  the  dis- 
persion of  sunliglit  by  rain-drops. 

The  spectrum  may  be  projected  upon  a  screen,  or  it  may  be 
received  directly  by  the  eye,  as  in  the  two  following  experi- 
inents :  — 


Experiment  3.  Upon  a  black  card-board  A  (Fig.  274)  paste  a  strip 
of  white  paper  .Sc"  long  and  2n..n  wide ;  and  ,>lace  the  prism  and  the  eye 
an  in  tlie  flgiire.  Now  a  beam  of  white  light  from  the  strip  is  refracted 
aiul  dispersed  by  the  prism,  and,  falling  upor  the  retina  of  the  eye,  you 
see,  not  the  narrow  white  strip  in  its  true  position,  but  a  spectruin  in 
the  position  A'.    This  experimenlj  is  performed  in  a  lighted  room. 

Kxperiment  3.     Instead  of  a  continuous  white  strip,   paste   short 
strips  of  red,  whi;e,  and  blue,  end  to  end,  on  the  black  card,  as  repre- 
sented  in   Fig.  275.     The   spectrum  of  each 
color  is  given  on  the  right,  the  light  portions 
rei)resenting    the    illumi- 
nated parts.  It  will  be  seen 
that  in  the  spectrum  of  the 
red,  the  green,  blue,  and 
violet  portions  are  almost 
completely  dark,  I)ut  there 
is  a  faint  trace  of  orange ; 

in  the  spectnim  of  the  blue, 

the  red,  orange,  and  yel- 
low are  wanting,  blue  and 

^'iolet  are  present,  and  a 

small  quantity  of  green. 

(What  lessons  does  this  ox[)eriment  teach  ?) 
Experiment  4.  —  In  place  of  the  wliite  strip 

of  paper  used  in  Exix;riment  2,  admit  light  into 

its  spectrum.  *  ^""''^  '"'''""  ""**'"^''  *  "^""'''^  ^"*'  *"'^  *^^''""»« 

§  304.  Synthesis  of  white  light.  -The  composition  of 
white  light  has  been  ascertained  by  the  oroccssof  an^i'-,-.  .  ean 
it  be  veriQed  by  syntheaiaf-^U.,  can  the  colors,  after  dispersion 


ents  which 
istration  of 
of  the  dis- 

it  may  be 
ng  cxpen- 


)aste  a  strip 
and  the  eye 
is  refracted 
lie  eye,  yoii 
ipectrmn  in 
room. 

)astc  short 
1,  as  repre- 
in  of  each 
ht  portions 

g.  275. 


COLOR  AND  DISPEllSION. 


359 


each  ?) 
iiitc  .strip 
li?j:ht  into 
1  examine 


sitiou  of 

Ola   •    *^*-»  •-» 

">•:■  i    Villi 

persion, 


1)6  reunited?  ;,ud,  if  so,  will  the  result  of  the  reunion  be  white 
liglit? 

Experiment  1.    Place  a  second  prism  (2)  in  such  a  position  AV  that 
light  which  has  passed  through  one  prism  (]),  and  l)een  refracted  and 
deconiposed,  may  be  refracted  bacl<,  ami  the  colors  will  be  reblended 
and  a  white  image  of  the  slit  will  be  restored  on  the  screen. 

Experiment  3.  Place  a  large  convex  lens,  or  a  concave  mirror,  so  as 
to  receive  the  colors  after  dispersion  by  a  prism,  and  bring  the  rays  to 
a  focus  on  a  screen.     What  is  the  color  of  the  image  produced? 

Experiment  3.  Receive  the  spectrum  on  a  common  plane  mirror 
and  rapidly  tip  the  mirror  back  and  fortli  in  small  arcs  at  right  angles 
to  the  path  of  the  light,  no  as  to  mingle  the  ditterent  colors  on  the 
screen.     What  is  the  result? 

§  305.  Cause  of  color  and  dispersion.  —  The  color  of  light 
is  determined  solely  hy  the  number  of  loaves  emitted  by  a  luminous 
body  in  a  second  of  time,  or  by  the  con-esponding  ivave-length.  In 
a  dense  medium  the  short  waves  are  more  retarded  than  the  longer 
ones;  hence  they  are  more  refracted.  This  is  the  cause  of  dis- 
persion. The  ether  waves  diminish  in  length  from  the  red  to 
the  violet.  As  pitcli  depends  on  the  numb^  f  aerial  waves 
which  strike  the  ear  in  a  second,  so  color  depencs  on  the  num- 
ber of  ethereal  waves  which  strike  the  eye  in  a  second.  From 
well-established  data,  determined  by  a  variety  of  methods  (see 
larger  works),  physicists  have  calculated  the  number  of  waves 
that  succeed  one  another  for  each  of  the  several  prismatic  colors, 
and  the  corresponding  wave-lengths  ;  the  following  table  con- 
tains the  results.  The  letters  A,  C,  D,  etc.,  refer  to  Fraunho- 
fijr's  lines. 


Dark  red A 

Orange C 


I.wigtli  of  waves 
iu  niilliinetci'8. 


No.  of  waves 
per  secoud. 

0<^07G0 iW5,000,00(),000,0()0 

,,  „  *^00C5() 458,000,000,000,000 

^^'"*^'^^' I^ 00058!) 5io.ooo.nnn  nno  ooo 

^'^:"" ^'^ 000527 570,000,000,000,000 

C-  Blue F 00048G 


U.  Blue G 


Violet... H. 


018,000,000,000,000 

■"•'0^=51 «!)7,000,000,000,000 

■000397 7G0,000,000,000,000 


5)H 

'ill 


360 


RADIANT  ENERGY. -—LIGHT. 


Tlioro  .H  a  limit  to  the  sensibility  of  the  eye  as  well  as  of  the 
enr.      I  !,„  l„„it  in  the  n.unber  of  vibrations  appreciable  by  the 
^0  Hen  approximately  within  the  range  of  numbers  given  in  the 
above  table  ;  U.,  if  the  succession  of  waves  is  much  more  or 
ess  rapid  tlmn  irulicate.l  by  these  numbers  thev  do  not  produce 
the  sensation  of  sight.     It  is  evident  that  the  frequency  of  the 
waves  emitird  h,,  «  haninous  hoOy,  and  consequently  the  color  of  the  ' 
lnj.te,,utl,d,mmt  depend  on  the  rapidity  of  the  vibratory  motions 
iphe  nolevub'H  of  that  body,  i.e.,  upon  its  temperature.     This 
has  b(.«M.  shown  in  a  convincing  manner  as  follows:  The  tem- 
perature of  a  platinum  wire  is  slowly  raised  l)y  passing  a  gradu- 
ally nK..rc.aHn.g  c.u-rent  of  electricity  through  it.     At  a  tempera- 
ure  of  alK,nt  540°  C.  it  begins  to  emit  light ;  and  the  light,  ana 
lyzed  by  a  pnsrn,  shows  that  it  emits  only  red  IwU.     As  the 
temperature  rises  there  will  be  added  to  the  red  of  the  spec- 
trum, first  yellow,  then  green,   blue,  and  violet  successively. 
When  It  reaches  a  white  heat  it  emits  all  the  prismatic  colors. 
It  18  signl  leant  that  a  white-hot  body  emits  more  red  light  than 
a  red-hot  body,  and  likewise  more  light  of  every  color  than  at 
any  lower  tomperature.     The  couclusion  is  that  a  body  which 
emus  white  light  sends  forth  simultaneously  waves  of  a  variety  of 

§  306.    Heat  and  chemical  spectra.  —  If  a  sensitive  ther- 
mometer ,s  placed  in  different  parts  of  the  solar  spectrum  it 
will  indicate  heat  in  all  parts ;  but  the  heat  generally  increases 
from  the  violet  toward  the  red.     It  does  not  cease,  however, 
with  the  limit  of  the  visible  spectrum;  indeed,  if  the  prism  is 
made  of  flint-glass,  the  greatest  heat  is  just  bevond  the  red      A 
strip  of  paper  wet  with  a  solution  of  chloride  of  silver  suffei-s 
no  change  in  the  dark  ;  in  tiie  light  it  quickly  turns  black  ;  ex- 
posed to  the  light  of  the  solar  spectrum  it  turns  dark,  but  quite 
unevenly.     The  changn  is  slowest  in  the  red,  and  constantly 
increases,  till  about  the  region  between  blue  and  violet,  when 
It  attains  its  maximum ;  from  this  point  it  falls  off  and  ceases 


ONLY  ONE  KIND  OF  RADIATION.  361 

at  a  point  cousiderably  buy«n,l  tf.o  limit  of  the  violet.  It  thi.s 
appears  that  the  solar  HiHK^tnun  is  not  limited  to  the  visible 
spectrnm  but  extends  beyond  at  each  extremity.     Those  ra 

wll  !  T^  ,""1  '"^  "''  "''"""y  ^'-^"^^^  '^^  ^^^^-red  rays, 
whde  those  that  he  beyond  tha  violet  arc  called  the  ultra-violet 

thr;,!.  ,  .    ;'f  '"^'  "•"  ^'  ^'^'^S^''  vibration-period,  and 

the  ultra-violet  of  shorter  in^rlcKl,  than  the  luminous  rays. 

§  307.  Only  one  kind  of  radiation. -The  fact  that  radi- 
ant energy  produces  three  dJHtinct  effects-viz.,  luminous 
heatmg,  and  chemical -ban  given  rise  to  a  quite  preva  eu  Tr.: 
that  there  are  three  distinct  kl„d«  of  nuliation.  There  is,  how- 
ever, absolute  y  no  proof  that  those  different  effects  are  produced 
by  different  kinds  of  radiation.     The  same  radiation  tkat  pro- 

frr.r'T  ""'^  ^'"''"^'  ^''^^  «^*^  chemical  action.     The  fact 
that  the  ultra-red  and  ultra-violet  rays  do  not  affect  the  eye 

th^r  W -T.     '  y  '''  "'  "  ^"^^^^"'  "^*-«  f-m  tho'se 

bihty  of  the  eye  to  receive  Impressions  from  radiation.     Just  as 

felVtn  Ttr"""  ""^  "^  '^"»'   '^"^  «*h^^«  ^'  too  short, 
period  to  affect  the  ear,  so  there  are  ethereal  waves,  some  o 

too  long  and  other,  too  short,  period  to  affect  the  eye.  I 
IS  true,  however,  that  wave«  of  long  period  from  the  sun  are 
more  energetic  m  producing  heating  effects  than  those  of  short 
penod  ;  and  those  of  short  period  are  more  effective  in  .vener- 
ating chemical  action  In  certain  substances  than  those  of  lon<. 
period  ;  while  only  those  which  lie  between  the  extremes  affect 

uUG  6YG* 


LVII.    COLOK. 
§  308.  Color  produced  by  abaomf.i.m  —  "  a  ii  ^.r^i^cts  -p 

^J^  ""  '"!^'"  "r'  '«^^i"ivale;;t"'to~saying';h7L7:;, 
hght  there  ^s  no  color.  U  color  a  quality  of  an  object,  or  is  it  a 
quality  of  the  light  which  Illuminates  the  object  ?" 


I 


862 


RADIANT  ENERGY. —.  LIGHT. 


Experiment  1.  Common  salt  Introduced  Into  a  Bunsen  flame  reudcr.s 
It  luminous,  and  the  light,  when  analyzed  with  a  prism.  Is  found  to 
contain  only  yellow.  Expose  papers  or  fabrics  of  various  colors  to  this 
light  in  a  darkened  room.  No  one  of  them  exhibits  its  natural  color  except 
yellow.  ,  ■' 

Experiment  2.    Hold  a  narrow  strip  of  red  paper  or  ril)bon  In  the 
red  portion  of  the  solar  spectnun;  ()l,ser\-e  its  color.     Slowly  move  it 
toward  the  otlier  end  of  the  spectrum,  carefully  observing  Its  appear- 
ance as  it  moves  througli  the  different  colors.     Uepeat  the  experiment 
using  other  colors.     Tabulate  the  results  of  these  experiments 


These  experiments  show  that  (1)  color  is  a  quality  of  the  light 
which  illuminates,  and  not  of  the  object  illuminated;  (2)  in  order 
that  an  object  may  appear  of  a  certain  color  it  must  receive  light 
of  that  color;  and  of  course  if  it  receives  other  colors  at  the  same 
time  it  must  be  cajmble  of  absorbing  them.     The  enei-gy  of  the 
waves  absorbed  is  converted  into  heat,  and  warms  th'e  object. 
Wiien  white  light  strikes  an  object  it  appears  white  if  it  reflects 
all  the  colors.     If  red  light  falls  upon  the  same  object  it  appears 
led,  for  it  U  capable  of  reflecting  red ;  or  it  appears  green  if 
green  light  alone  falls  on  it.     If  white  light  falls  upon  an  object, 
and  all  the  colors  are  absorbed  except  the  blue,  the  object 
appears  blue.     When   we  paint  our  houses  we  do  not  apply 
color  to  them.    We  apply  substances,  cvi\\ei\ pigments,  that  have 
a  property  of  absorbing  all  the  colors  except  those  which  we 
would  have  our  houses  appear. 


Experiments.    By  means  of  mporte  lumih-e  introduce  a  beam  of 
hght  into  a  dark  room.     Cover  the  oriflce  with  a  deep  red  (cot.per)  -lass 
Tlie  white  light,  in  passing  through  the  glass,  appears  to  be  colored 
red.     Does  the  glass  color  the  light  red  t 

P..perm>.ent  4.  With  the  slit  and  prism  form  a  solar  spectrum,  and 
between  the  prism  and  screen  interpose  the  red  glass.  What  is  the  re- 
sult?   Ddes  the  glass  color  the  light?    If  not,  what  does  the  glass  do' 


THERMAL   EFFECTS   OP  RADIATION. 


363 


I  flame  rcutlcrs 
1,  Is  found  to 
1  colors  to  this 
'al  color  except 

ribbon  in  tlic 
lowly  move  it 
ij,'  its  appoar- 
j  cxporiinont, 
lents. 


/  of  the  light 

(2)  in  order 

receive  light 

at  the  samp. 

ergy  of  the 

the  object. 

if  it  reflects 

t  it  appears 

rs  green  if 

a  au  object, 

the  object 

not  apply 

J,  that  have 

3  which  we 


a  beam  of 
l)per)  glass. 
3  be  colored 


tjctrum,  and 
It  is  the  re- 
3  glass  do? 


LIX.     THERMAL  EFFECTS   OF   RADIATION. 

§  30a  Diathermancy  and  athermancy.  —What  becomes 
of  radiations  that  strike  a  body  depends  largely  upon  the  char- 
ucter  of  the  body.     If  the  nature  of  the  body  is  such  that  its 
molecules  can  accept  the  motion  of  the  ether,  the  undulations 
of  ether  are  said  to  l)e  absorbed  by  the  body,  and  the  body  is 
thereby   heated ;    that  is,  the  undulations  of  ether  are  trans- 
formed into  molecular  motion  or  heat.     A  good  illustration  of 
this  is  the  experiment  with  blackened  glass,  page  321.     On  iJie 
other  hand,  the  unblackcned  glass  allows  the  radiations  to  pass 
freely   through   it,  and  very  little  is   transformed   into   heat. 
Notice  how  cold  window-glass  may  remain,   while  radiations 
pour  through  it  and  heat  objects  within  the  room.     It  must  be 
constantly  borne  in  mind,  that  only  those  radiations  that  a  body 
absorbs  heat  it;  those  that  pass  through  it  do  not  affect  its  tern- 
perature.     Bodies  that  transmit  radiant  heat  freely  are  said  to 
be  diathermanoiis,  while  those  that  absorb  it  largely  are  called 
athertnanous.      The   most   diath-       nous   solid    is    rock    salt. 
Among  the  most  athermanous  solu     are  lamp-black  and  alum. 
Carbon  bisulphide,  among  liquids,  is  exceptional^'  transparent 
to  all  forms  of  radiation;  while  water,  transparent  to  short 
waves,  absorbs  the  longer  waves,  and  is  thus  quite  athermanous. 

Expertment  1.  Bring  the  bulb  of  an  air  thermometer  into  the 
focus  of  a  burning-glass  exposed  to  the  sun's  rays.  The  radiation 
concentrated  on  the  enclosed  air  scarcely  affects  this  delicate  iustru- 
nient. 

Experiment  2.  Cover  the  outside  of  the  bulb  of  the  air  thermom- 
eter with  lamp-black  and  repeat  the  last  experiment.  The  lamp-black 
absorbs  the  radiant  heat,  and  the  heat  conducted  through  the  glass  to 
the  enclosed  air  raises  its  temperature  and  causes  it  to  expand  and 
rapidly  push  the  liquid  out  of  the  stem. 

Dry  air  is  almost  perfectly  diathermanous.     All  of  the  sun's 

'■  -"^  eartn  paaa  mruugh  a  layer  or  air,  from 

fifty  to  two  hundred  mUes  in  depth,  which  contains  a  vast 


ii 


864 


RADIANT  ENERGY.  —  LIGHT. 


;. 


an»„„t  of  aqnoom  vapor.    This  vapor,  like  water,  is  compara- 
tively  opaque  to  long  waves;  Iience  it  modifies  very  ITtte 
el:aracter  of  tbe  radiations  whiol,  reach  the  earth,     nlfalt 
together  w.th  what  we  have  learned  from  Exp.  2,  enablf  „' 

1^  T,  *"'  ""'""^  "^  "'■'■'^  0"  atmosphee  become 
heated.  First,  a  very  considerable  portion  of  the  radiant  re^v 
which  comes  to  us  from  the  sun,  in  the  form  of  relat"veirro™ 
«ves,  i,  stopped  by  the  watery  vapor  in  the  air  w^Lti  f 
^..sequence,  heated.  Most  of  that  which  escape  tW  ab  onT 
^on  heats  the  earth  by  falling  upon  it.  The  warmed  eartht!, 
■ts  heat,  _  partly  by  conduction  to  the  air,  still  more  at  ll  bv 

rre::ht:erd^tra;-2^^^^^^^^ 

waves  „Meh  are  most  readily  stopped  by  the  a  mospLr  flic? 
«  e  atmosphere  or  rather  the  aqneous  vapor  of  the  atmCe  e 
ate  as  „  sort  of  trap  for  the  energy  which  comes  to  us  fim  the 
sun  Remove  the  watery  vapor  (which  serves  as  a  "  blanket  " 
to  the  earth)  from  our  atmosphere,  and  the  chill  result!  g  from 
the  r.ap,d  escape  of  heat  by  radiation  would  put  an  end  toT 

TuT LT  bTT "'"  '""'^  "^'  ■'°'  Lee::i:z 

riat  d  L™         '""'  ""^  '""'"""'"^'  ^'"■«'=°  "^  "•<»"  ">e  heat 
radiated  from  a  stove  or  any  other  terrestrial  object.    Glass  is 

diathermanous  to  the  sun's  radiations  (simply  because  thev 

T::tXaT ::  "^  ^^^^  '--^  -e^byroVe- 

absoipton),  but  quite  athermanous  to  other  radiations.    This 

Thrf  nth!:      '"  *^  ""  "'  ""'-"""^  »»•  greeu-hou! 
1  be  sun  s  heat  passes  through  the  glass  of  these  enclosure, 
almost  unobstructed,  and  heats  the  earth,  but  the  »us 
pven  out  in  turn  by  the  earth  are  such  as  cannot  m  s  Z 
thtougb  tte  glass,  hence  the  heat  is  retataed  wi^i:  ^1^ 


,  is  compara- 
ry  much  the 
This  fact, 
2,  enable  us 
ere  becomes 
diant  energy 
atively  long 
which  is,  in 
this  absorp- 
i  earth  loses 
e  largely  by 
Br,  has  been 
low  temper- 
ransmitted ; 
short  waves 

these  Ions: 
sre ;  hence, 
itmosphere, 
us  from  the 
"  blanket " 
ilting  from 

end  to  all 
IS  from  the 
m  the  heat 
Glass  ia 
!ause   they 
tmospheric 
ms.     This 
en-houses, 
nclosures, 
radiations 

pass  out 
the  endo 


GOOD  ABSORBERS. 


365 


§  ^10.  All  bodies  radiate  heat.  —  Hot  bodies  umally  part 
with  their  heat  much  more  rapidly  by  radiation  than  by  all  other 
processes  combined.  But  cold  bodies,  like  ice,  radiate  heat  even 
when  surrounded  by  warm  bodies.  This  must  be  so  from  the 
nature  of  the  case,  for  the  molecules  of  the  coldest  bodies, 
possess  some  motion,  and  being  surrounded  by  ether,  they  can- 
not move  without  imparting  some  of  their  motion  to  the  ether, 
and  to  that  extent  losina:  some  of  their  own  motion. 

§  31L  Theory  of  Exchanges.  —  Let  us  suppose  that  we 
have  two  bodies,  A  and  B,  at  different  temperatures,  —A  warmer 
than  B.  Radiation  takes  place  not  only  from  A  to  B,  but  from 
B  to  A  ;  but,  in  consequence  of  A's  excess  of  temperature,  more 
heat  passes  from  A  to  B  than  from  B  to  A,  and  this  continues 
until  both  bodies  acquire  the  same  temperature.  At  this  point 
radiation  by  no  means  ceases,  but  each  now  gives  as  much  as  it 
receives,  and  thus  equilibrium  is  kept  up.  This  is  known  as 
the  "  Theoi-y  of  Exchanges." 

§  312.  Good  absorbers,  good  radiators.  —  Experiment. 

Select  two  small  tin  boxes  of  equal  capacity,  —  one  should  be  bright  out- 
side, while  the  other  should  be  covered  thinly  with  soot  from  a  candle 
flame.  Cut  a  hole  in  the  cover  of  each  box  large  enough  to  admit  the 
bulb  of  a  thermometer.  Fill  both  boxes  with  hot  water,  and  introduce 
into  each  a  thermometer.  They  will  register  the  same  temperature  at 
first.  Set  both  in  a  cool  place,  and  in  half  an  hour  you  will  find  that 
the  thermometer  in  the  blackened  box  registers  several  degrees  lower 
than  the  other.  Then  fill  both  with  cold  water,  and  set  them  in  front 
of  a  fire  or  in  the  sunshine,  and  it  will  be  found  that  the  temperature 
in  the  blackened  box  rises  fastest. 

As  bodies  diflTer  widely  in  their  absorbing  power,  so  they  do 
m  their  radiating  power,  and  it  is  found  to  be  universally  true 
that  good  absorbers  are  good  radiators,  and  bad  absorbers  are 
bad  radiators.  Much,  in  both  cases,  depends  upon  the  charac- 
ter of  the  surface  as  well  as  the  substance.  Bright,  polished 
surfaces  are  poor  absorbers  and  poor  radiators  ;  while  tarnished, 
dark,  and  roughened  surfaces  absorb  and  radiata  heat  rapidly. 


^:| 


866 


RADIANT  ENEUGY.  — LIGHT. 


Dark  clothing  absorbs  and  radiates  heat  more  rapidly  than  light 
(Which  IS  better  to  wear  at  all  seasons?  Why?  Why  are  cer 
tarn  parts  of  steam  engines  kept  scrupulously  bright?) 

fZ^^^'  ^T'  ~  ^^''^"''"^"^  °°  •^l^borate  experiments  to  show 
that  some  bod.es  radiate  heat  more  rapidly  than  others.  AH 
nature  testifies  to  this  every  still,  cloudless  summer  night.  Dur- 
.ng  the  day  objects  on  the  earth's  surface  receive  more  heat  bv 
radiation  than  they  lose    but  -m  «nnn  no  fi  .  ^ 

isrPvPr«,pH  T.  '°^®'  '^"'^  '^«  soon  as  the  sun  has  set  this 
IS  rev  crsed.  Then  everything  begins  to  cool  as  its  heat  is  radi- 
ated mto  space.  Objects  becoming  cool,  the  air  in  contact  with 
hem  becomes  chilled  ;  its  watery  vapor  condenses,  and  colli  ts 
in  tiny  hquid  drops  on  their  surfaces.  But  these  dew-drops 
CO  ect  much  more  abundantly  on  certain  things,  such  as  grasse 
and  leaves,  than  on  others,  such  as  stones  and  earth  The 
reason  that  it  does  not  collect  on  the  latter  so  freely,  is  because 
of  their  poor  radiating  power ;  they  do  not  get  cool  Js  rapid" 

Fig.  294. 


LX.     SOME   OPTICAL   INSTRUMENTS 

oLject  a.ore  than  oa,.  be  done  convonic,,  y^^':,  rf™^:;' 
"ess  by  a  »,„gfc  ,e,„,  two  convex  huso,  are  ."ed  -1?^ 
H-  2^4)  called  t.e  o.;.c<y«,  to  fora.  a  n^I^ZLSL^^ 


ASTRONOMICAL   TELESCOPE. 


367 


lly  than  light. 
»Vhy  are  cer- 
t?) 

ents  to  show 
others.     All 
night.     Dur- 
nore  heat  by 
has  set  this 
heat  is  radi- 
contact  with 
and  collects 
3  dow-droi)s 
li  as  grasses 
earth.     The 
',  is  because 
as  rapidly. 


microscope 
liagnify  an 
h  dfstinct- 
—  one  (O, 
real  image 


A'B'  of  the  object  AB  ;  and  the  other  (E)  called  the  eye-glass, 
to  magnify  this  image  so  that  the  image  A'B'  appears  of  the  size 
A"B".  In  the  same  sense  as  we  look  at  the  object  with  one 
lens  when  we  use  a  simple  microscope,  here  we  look  at  A'B'. 

§  315.  Astronomical  telescope.  —  The  astronomical  re- 
fracting telescope  consists  essentially,  like  the  compound  micro- 
scope, of  two  lenses.  The  object-glass  (O,  Fig.  29o)  forms  a 
real  diminished  image  ab  of  the  object  AB;  this  image,  seen 
through  the  eye-glass  E,  appears  magnified  and  of  the  size  cd. 
The  object-glass  is  of  large  diameter,  in  order  to  collect  as 
much  light  as  possible  from  a  distant  ol)ject  for  a  better  illumi- 
nation of  the  image.     Some  idea  of  the  power  of  some  of  our 


Pig.  295. 


best  telescopes  may  be  obtained  from  the  fact  that  Mr.  Clark 
of  Cambridgeport  has  made  a  telescope  of  such  magnifying 
power,  and  possessing  such  distinctness  of  definition,  that  a  ball 
two  inches  in  diameter,  and  two  hundred  and  fifty  miles  distant 
(about  the  distance  i)etween  Boston  and  New  York),  would  be 
difetiuctly  visible  as  a  body  of  perceptible  dimensions,  if  properly 
illuminated. 

§  316.  Photographer's  camera.  —  Tlie  ]ihotographer's  cam- 
era, or  ca.mp.ra  ohscura,  of  which  AB,  Figure  20G,  represents  a 
vertical  section,  consists  of  a  dark  box  painted  black  on  the 
interior.     A  screen  of  ground  glass  S  forms  a  partition  in  the 


S68 


I 


RADIANT  ENERGY.  —  LIGHT. 


box.     A  sliding  tube  T  contains  a  convex  lens  T      if        u-    . 
r>  IS  placed  some  distance  in  front  and  fL  !i   .  °  ""^J"'* 

from  the  screen  is  suitably  adjS'  a  dt  tt       f'  1  • ''  '"' 
image  can  be  seen  nnon  ,?''' '^'^*'^°*' ^^^1' and  inverted 

aperture  C.  Vhl  Zlntl  ''"'"  '^  ^°°'^"^  ^^^-g^  the 
grapher  replaclte  g  ur|L::  ZTl  '"""''  •''  '''''^■ 
and  the  chemical  power  of  thf  sun'f  ^  '  '''''•*'''^  P'^^' 

of  the  object  on  this  plate!  '"  ^""'^  "  *^«  ^'^^^^ 

Fig.  296. 


Fig.  297. 


called  the  cornea.  A  tough  membrane 
2,  of  which  the  cornea  is  a  continua- 
tion,  forms  the  outer  wall  of  the  eye 
and  Is  called  the  sclerotic  coat,  or 
"  white  of  the  eye."     This  coat  is 
liued  ou  the  interior  with  a  delicate 
membrane  3,  called  the  choroid  coat; 
the  latter  is  covered  with  a  black 
pigment,   which   prevents    internal 
reflection.    The  inmost  coat  4,  called 
«ie  mma,  is  formed  by  expansion 
Of  the  optic  nerve  0.     The  front  of 
the  choroid  coat  ii  is  called  the  Ms; 
Its  color  constitutes  the  so-called 

can:d7::trw;oseVut^^^^^^^^^^ 

ment  and  contraction,  the  ,uJtV/o7t^:±ZfTr^^^^^^^^ 
vfiamDcr  oi  ihe  eye.     Just  hnov  ^f  *\.    7  ,     . '"'  ""^  "itcnor 

transparent  body  6  called  .>•,        "  ^  *°"^'''  '^*'"''  "^^^ 

ay  6,  called  the  crystalline  lens.    This  lens  dlvldei  the 


If  an  object 
;e  of  the  lens 
and  inverted 
through  the 
i,  the  photo- 
litized  plate, 
true  picture 


HUMAN  EYE, 


869 


Z3 


a  horizontal 
le  eye,  like  a 


opening  5, 
•y  enlarge- 
ic  Interior 
astic,  and 
ivldes  the 


eye  into  two  chambers ;  the  anterior  chamber  7  is  filled  with  a  limpid 
Uquid,  called  the  aqnenus  humor;  tlie  posterior  chambei  8  is  filled  with 
a  jelly-lilie  substance,  called  the  vitreous  humor. 

The  eye  is  a  cnmora  obscura,  in  which  the  retina  serves  as  a 
screen.     Images  of  outside  objects  are  projected  by  means  of 
the  crystalline  Ions,  assisted  by  the  refractive  powers  of  the 
humors,  upon  this  screen,  and  the  impressions  thereby  made  on 
this  delicate  network  of  nerve  filaments  are  conveyed  by  the 
optic  nerve  to  the  brain.    Jf  tlie  two  outer  coatings  are  removed 
from  the  back  part  of  the  eye  of  an  ox,  recently  killed,  so  as  tO 
render  it  somewhat  transparent,  true  images  of  whole  land- 
scapes may  bo  seen  formed  upon  the  retina  of  the  eye,  when  it 
is  held  in  front  of  your  eye.     With  the  ordinary  camera,  the 
distance  of  the  li-ns  from  the  screen  must  be  regulated  to  adapt 
itself  to  the  varying  distances  of  outside  objects,  in  order  tliat 
the  images  may  bo  i>rop(!rly  focused  on  the  screen.     In  the  eye 
this  is  accomplished  by  changing  the  convexity  of  the  lens.    We 
can  almost  instantly  and  involuntarily  change  the  lens  of  the 
eye,  so  as  to  form  on  the  retina  a  distinct  image  of  an  object 
miles  away  or  only  a  few  inches  distant.     The  nearest  limit  at 
which  an  object  can  be  placed,  and  form  a  distinct  image  on  the 
retma,  is  about  five  inches.     On  the  other  hand,  the  normal  eye 
m  a  passive  state  is  adjusted  for  objects  at  an  infinite  distance. 
Curious  enough,  the  retina  on  careful  examination  is  found  to 
be  covered  with  little  projections  which  have  received,  from 
their  appearance,  the  names  of  rods  and  cones.     These  project 
from  the  nerve  fibres  very  much  like  nap  from  the  threads  of 
velvet.     It  is  thought  that  these  rods  and  cones  receive  and 
respond  to  the  vibrations  of  light ;  in  other  words,  that  they 
co-Tibrate  with  the  undulations  of  the  ether,  and  thereby  we  get 
our  sensation  of  light. 

.  .  _.hromatio  aberration.  —  There  is  a  serious  defect 
in  ordinary  convex  lenses,  to  which  we  have  not  before  alluded, 
caUed  chromatic  aberration,  which  has  required  the  highest  skill 


370 


RADIANT  ENERGY.  —  LIGHT. 


Of  man  to  correct.     The  c6nvex  lens  both  refracts  and  disperses 
the  hght  that  passes  through  it.     The  tendency,  of  course,  is  to 
bring  the  more  refrangible  rays,  as  the  violet,  to  a  focus  much 
sooner  than  the  less  refrangible  rays,  such  as  the  red.     The 
result  IS  a  disagreeable  coloration  of  the  images  that  are  formed 
by  the  lens,  especially  by  that  portion  of  the  light  that  passes 
through  the  lens  near  its  edges.     This  evil  has  been  overcome 
very  effectually  by  combining  with  the  convex  lens  a  plano-con- 
cave lens.     Now,  if  a  crown-glass  convex  lens  is  taken, 
a  flint-glass   concave   lens  may  be  prepared  that  will 
correct  the  dispersion  of  tlie  former  without  neutralizing 
all  its  refraction.'    The  possibility  of  this  is  due  to  the 
fact  that  flint-glass  disperses  more  strongly  in  propor- 
tion to  its  refractive  power  than  crown-glass.     A  com- 
lK)und  lens,  composed  of  these  two  lenses  (Fig.  298) 
cemented  together,  constitutes  what  is  called  an  achromatic  lens. 

Fig.  299. 


Fig.  2n8. 


§  319.  Stereopticon.  —  This  instrument  is  extensively  em- 
ployed in  the  lecture-room  for  producing  on  a  screen  magnified 
images  of  small  transparent  pictures  on  glass,  called  dides; 
also  for  rendering  a  certain  class  of  experiments  visible  to  a 
large  audience  by  projecting  them  on  a  screen.  The  light  most 
commonly  used  is  the  lime  light,  though  the  electric  light  is  pre- 
ferred for  a  certain  class  of  projections.  The  flame  of  an  oxyhy- 
drogen  blow-pipe.  A,  Fig.  299,  is  directed  against  a  stick  of 
lime  B,  and  raises  it  to  a  white  heat.  The  light  of  the  lime  is 
converged-^ by  means  of  a  convex  lens  c,  called  the  condensing 

>  The  refractiTe  and  dliperiire  pow«r.  of  the  two  Iot««i  are  not  proporUon.1. 


CHROMATIC    ABBE  RATION. 


371 


Ffg.  208. 


lens  (usually  two  plano-convex  lenses  are  used)—  upon  the  slide 
D,  and  strongly  illuminates  it.  In  front  of  it  is  placed  another 
convex  lensE,  (or  a  system  of  lenses),  called  the  projecting  lens. 
Tlie  latter  lens  produces  (or  projects)  a  real,  inverted,  and 
magnified  imago  of  the  picture  on  the  screen  S.  The  n^ounted 
lens  E  may  be  slid  back  and  forth  on  the  bar  F,  so  as  properly 
to  focus  the  image.  (For  useful  information  relating  to  the 
operation  of  projection,  see  Dolbear's  Art  of  Projection.) 


¥?• 


APPENDIX. 


bnnik: 

jTMIIIInMUn. 


Inehe*. 


J5 |6_ 


CeutUneten. 


Sqiur* 
Oentimttw 


The  area  of  this  figure  is  a  square  decimeter. 
A  cube  of  water,  one  of  whose  sides  is  this  area, 
Is  a  cubic  declmster  or  a  liter  of  water,  and  at  the 
temperature  of  4"  C.  weighs  a  kilogram.  The 
same  volume  of  air  at  0"  C,  and  under  a  pressure 
of  one  atmosphere,  weighs  1.293  grams.  The 
mm  is  the  weight  of  loo  of  pure  water  at  4'  C. 


th< 
in 
of 
mi 
l)e 
on 
ret 
of  1 
At 
mei 

puj 


Square  Inch. 


J8 l»  HI 


S, 


Square  Inch. 


APPENDIX. 


BHOTION  A. 

measures  ^  *"®  ™®*®^  *"**  o*^her  metric 

TABLE  OF  LENGTHS. 

10  mllllmeten.  (mm)  _  j  centimeter  (-cmV 
OceutimetorH  -  1  decimeter  (W. 

lOdeclmeterB  =  1  meter  fm) 

1000  meters  ^  ,  k„ometer  (k»). 

TABLE  OF  AREAS, 


100  square  mllllmeter»  («mm^  ^  i  „n„„r„  „„„«      x      , 
100  square  centimet«rl  i  ^         centimeter  (icm). 

100  -  -        cenumet«r«  ==  i  square  decimeter  rqdmv 

—  i  square  meter  (•>">). 

=  1  square  Jcilometer  (Qkm). 


1,000,000  square  raeteri 


370 


APPENDIX. 


TABLE  OP  VOLrTMES. 

1000  cubic  millimeters  (-m)  .  ,  cubic  centimeter  (-'or-) 
000  cub  c  centimeters  =  i  cubic  decimeter  (L^ 

1000  cubic  decimeters  =  1  cubic  meter  (cbm;.     ^ 

oflllrr^^'Tn^  ^"l»i''«  and  gases  are  either  expressed  in  t],.  ,  nita 
of  the  above  table  or  in  liters.     The  liter  is  Icdm,  ^r  lOOoV 


TABLE  OP  MASSES  OR  WEIGHTS. 

10  milligrams  (-"«)  =  i  centigram  (eg). 
10  centigrams         =  i  decigram  ^<i«). 
10  decigrams'  =  i  gram  (k). 

1000  grams  =  i  kilogram  or  kilo  (k). 

TABLE  OF  EQUIVALENTS. 
1  inch  =       0.0254  meter,    or  about  2J  centimeters. 

yard!       0    u^r-    -'^''-*  30  centimeters, 
iyard-       0.9144  meter,    or  ai)out  {?  meter 
1  m.le  =  1609.0000  meters,  or  about  l^  kilometers. 

1  U.S.  ^  "^"^<^  quart  =  ^  0.946  liter,    „  ,.^^,     .  igg^ 

1  dry     y  1  1.101  liters,  ""  J'"Ie  {  JJ^^^  than  1  liter; 

1  U.S.  gallon  =  8.785  liters,  or  about  3/^  liters. 

1  J  avoirdupois  .   ^no^.-  ,  ., 

^  Troy  and  apothecaries'  ounce  =  <{  0.(L-;;  1<.  o,  .^ rather  <[ 
than  30  grams. 

1  avoirdupois  pound  =  0.46359  kilo,  or  about  ^^  kilo. 

reriTat'"""^  ''  "°*"^^^^^^'  ''  -"  ^  ^-"^  convenient  to 

centimeters  x  f  =  inches  (nearly)  ; 
inches  X  f  =  centimeters  (nearly)  • 

5  meters  =  1  rod  rnearlv^  • 

^so,  kilos  XV  =  pounds  (nearly); 

pounds        XA  =  kilos  (nearly). 


less 
more 


APPENDIX, 


877 


["'"'or'"). 


in  tlie  units 


). 

eters. 
eters. 

eters. 

liter; 

;her  <{ 


less 
more 


iveuient  to 


Fie.  aoo. 


SECTION  B. 

nl.?"*!"'"*  firlasB. -Bottoms  of  glass  bottles  may  be  cut  off  an  J 
f^J       r'.""'  '"'"^^"*  ^"  any  pattern  desirable!  by  observL  the 

xpos  d   nd  be  filedt       '     Z  """i  ^"  "  "°'^'^^"  ^'"'^•^  ^'  ^"d  let  the 
exposed  end  be  fi  ed  to  a  smooth  surface.    With  a  poi  nted  piece  of  soap 

ace  a  Ime  on  the  glass  where  you  would  cut;  and   if  it  is  a  boS 

nt::  vt  ZT ' ''-'  ^-'  ^  (-  ^  ^^p^^  -^'-'  >vith ;:  s 

in  the  bottle  in  the 

direction    of    the 

line  drawn.    Heaf, 

in  a  Bunsen  flame, 

the  free  end  of  the 

rod  to  a  bright  red 

heat    (the    hotter 

the    better),    and 

apply  the    heated 

end  to  the  glass,  as 

in  the  figure  about  l™-  from  one  extremity  of  the  gash  for  (.  v)  about 

the  other  extremity  of  the  gash,  as  D,  and  hold  it  firmly  til.   ,-ou  see 
a  fine  crack  creepmg  toward  the  rod;  then  slowly  move  the  re     aW 

^L!       !,  ^        ^^^''  ''  *°  ^"  ^"*'  fil«  ^  «"^^"  gash  E    ,1  one 

edge,  and,  commencmg  with  this  gash  as  before,  you  may  cut  in  the 

f  r  It'  Z  ""^  ^'"^"  y°"  '^^^^^^^     T«  ^--^  ho>e«  in  glass,  make 
;  ei  S  '         ^^  Pf  "^^^  '""^^"^  ^^"^  «^-Phor  in  splits  o:  tur! 
pentme,  mp  off  a  short  piece  from  the  end  of  a  small  rat-tail  file 
and  keeping    he  ragged  end  wet  with  the  paste,  you  can  readily    or 
a^hde  by  employmg  strong  pressure,  and  by  a  twisting  movemenc  al 


378 


APPENDIX. 


pi 


''1 

SECTION  O. 

TABLES    OP   SPECIFIC    GRAVTriES   OP   BODIES. 
[The  standard  employed  in  the  tables  of  solids  and  liquids  is  distilled  water  at4*C.] 

I.   Solids. 


Antimony 6.712 

Bismuth 9.822 

Brass 8.380 

Copper,  cast 8.790 

Iridium 23.000 

Iron,  cast 7.210 

Iron,  bar 7.780 

Gold 19.360 

Lead,  cast ]  1.350 

Platinum 22.069 

Silver,  cast 10.470 

Tin,  cast 7.290 

Zinc,  cast 6.860 

Anthracite  coal 1,800 

Bituminous  coal 1.250 


Diamond 3.530 

Glass,  flint 3.400 

Human  body 0.890 

Ice 0.920 

Quartz 2.650 

Rock  salt 2.257 

Saltpetre 1.900 

Sulphur,  native 2.033 

Tallow 0.942 

Wax 0.9G9 

Cork 0.240 

Pine 0.650 

Oak 0.846 

Beech 0.852 

Ebony i.i87 


II.    Liquids. 


Alcohol,  absolute 0.800 

Bisulphide  of  carbon 1 .  293 

Ether 0.723 

Hydrochloric  acid 1.240 

Mercury 13.598 

Milk 1.032 

Naphtha 0.847 


Nitric  acid 1.420 

Oil  of  turpentine 0.870 

Olive  oil 0.915 

Sea  water 1.026 

Sulphuric  acid 1.841 

Water,  4°  C. ,  distilled ...  1 .000 

Water,  0°  C. ,  distilled  0.999 


Air 1.0000 

Ammonia 0.5367 

Carbonic  acid 1.5290 

Chlorine 2.4400 

Hydrochloric  acid 1.2540 


III.    Gases. 
[Standard  :  air  at  0°  C. ;  barometer,  76<n».] 

Hydrogen    0.0693 

Nitrogen 0.9714 

Oxygen 1.1057 

Sulphuretted  hydrogen  .  1.1912 

Sulphurous  acid 2.2474 


APPENDIX. 


379 


s. 


water  at  4*  C] 


3.630 
3.400 
0.890 
0.920 
2.650 
2.257 
1.900 
2.033 
0.942 
0.9C9 
0.240 
0.650 
0.846 
0.852 
1.187 


1.420 

0.870 
0.915 
1.02G 
1.841 
1.000 
0.999 


...  0.0693 

..  0.9714 

. ..  1.1057 

n  .  1.1912 

. ..  2.2474 


SECTION  D. 

TABLE  OF  NATURAL  TANGENTS, 


Deg. 

Tangmt. 

Deg. 

Tangent. 

Deg. 

Tangent. 

Deg. 

Tangent. 

I 

.017 

24 

.445 

47 

1.07 

70 

2.76 

2 

.036 

25 

.466 

48 

1.11 

71 

2.90 

3 

.052 

26 

.488 

49 

1.16 

72 

3.08 

4 

.070 

27 

.610 

50 

1.19 

73 

3.27 

6 

.087 

28 

.632 

61 

1.23 

74 

3.49 

6 

.105 

29 

.664 

52 

1.28 

75 

3.73 

7 

.123 

30 

.677 

53 

1.33 

76 

4.01 

8 

.141 

31 

.601 

54 

1.38 

77 

4.33 

9 

.168 

32 

.626 

65 

1.43 

78 

4.70 

10 

.176 

33 

.649 

m 

1.48 

79 

6.14 

11 

.194 

34 

.675 

57 

1.64 

80 

5.67 

12 

.213 

36 

.700 

58 

1.60 

81 

6.31 

13 

.231 

36 

.727 

69 

1.66 

82 

7.12 

14 

.249 

37 

.754 

60 

1.73 

83 

8.14 

15 

.268 

38 

.781 

61 

1.80 

84 

9.51 

16 

.287 

39 

.810 

02 

1.88 

85 

11.43 

17 

.306 

40 

.839 

63 

1.96 

86 

14.30 

18 

.325 

41 

.869 

64 

2.06 

87 

19.08 

19 

.344 

42 

.900 

65 

2.14 

88 

28.64 

20 

.364 

43 

.033 

66 

2.25 

89 

57.29 

21 

.384 

44 

.966 

67 

2.36 

90 

Inflnite. 

22 

.404 

45 

1.000 

68 

2.48 

> 

23 

,424 

46 

... 

1.036 

69 

2.61 

880 


APPENDIX. 


m^' 


^^^i^! 


SECTION  B. 

Galvanometer.  — A  galvanometer  that,  along  with  the  one  de- 
scribed in  §175,  will  answer  sufficiently  well  all  the  purposes 
of  this  book  can  be  easily  and  cheaply  prepared  as  follows: 
Make  a  wooden  frame  A  (Fig.  301).  iQcm  square  and  2.5o.n  thick, 
joined  by  wooden  or  brass  pins  in  grooves;  on  it  wind  50  to  00 
turns  (i  lb.)  insulated  No.  ICy  wire  in  two  layers,  leavin-  !<='» 
space  m  the  center  (in  the  figure  this  space  is  exaggerated  in-order 
to  show  the  position  of  the  needles),  and  insert  the  extremities  in  .'-r. 
brass  screw-cups  L  and  K.  In  this  frame  insert  a  copper  or  brass 
wire  D,  carrying  a  cork  E,  which  supports  a  silk  fibre  F  and  x  strip  of 

Fig.  301. 


n,T.  f h"  ?^^^"'*r  ^.  ^^"■S^  ««^ving-needle  II,  and  insert  in  the  paper, 
as  m  the  figure;  also  insert  a  small  copper  wire  I  in  the  paper  for  a 
pointer,  and  suspend  the  whole  so  that  the  needle  will  swing  freely 
between  the  upper  and  lower  windings  of  wire,  and  the  pointer  will  be 
just  above  the  coils.  Prepare  a  graduated  circle  on  a  card  M.  havintr 
a  hole  m  the  center  through  which  to  pass  the  needle,  and  lay  it  on  the 
coiL  To  prevent  disturbance  from  currents  of  air,  cover  the  whole 
with  a  frame  N,  haying  a  glass  plate  O  laid  over  its  top.  Connect  the 
battery  wrres  with  the  screw-cups  L  and  K.  The  cost  of  material  need 
not  exceed  75  cents. 


APPENDIX. 


381 


he  one  de- 
le  purposes 
IS  follows : 
2.o"»  thick, 
id  50  to  (]0 
e:ivin,if  V" 
ed  in  order 
lities  in  t'^o 
sr  or  br<ass 
d  ,i  strip  of 


SECTION  F. 

i'nportant  of  these  are  t"^    !'.>?"  "''"     ^"^"^  *^«  "-«* 

service  required     L     wwV^^  ""^  '"'"'"'"*  '"^^""•^J'  ^'iJ  the 
i«iiuirea,   i.e.,  whether  continuous,  temoorarv    r.r.  ■       , 

currents  are  wanted.     The  cost  i«  «f  'temporary,  or  occasional 

governed  mainly  bv  the  Z^Ta-  ««f  ^^"^"ce'  but  that  must  be 

arrangement  preference,  7       ^^  considerations.     In  the  following 

bers,   -n   the  Tdt  TwM^Thev       ^'^  "^"^^  '^"^"^^  ^^  ""- 
specified.—  ^'^  °''^  ^g*^"«*  tbe  several  uses 


1.  Smee. 

2.  Leclanche. 

3.  Gravity. 


NAJfES   OP   BATTERIES,   ETC. 


4.    Dauiell. 
Grenet. 


5. 


C.   Bunsen  or  Grove. 


7.  Magneto    or    dy- 

namo machines. 

8.  Thermo-batteries. 


;he  paper, 
per  for  a 
ng  freely 
er  will  be 
I,  having 
it  on  the 
he  whole 
anect  the 
rial  need 


USES  CELLS  ARE  SUITED  FOR. 
Strong,  Continuous  Currents. 

Electrotypiug  or  Electro-plating 

Electro-magnets 7,  4,  1,  3. 

Electric  light 3,  4,  1. 

Telegraph  (closed  circuit)  ........!...... ! '  ^" 

Temporary. 

Induotion  coils 

Medical  coils . .  S,  6,  4,  3. 

5,1. 


Occasional. 

Annunciators,  domestic  bells 

Exploding  fuses 

Eleetficui  measureiueuts  (constant  current) 


2,  1,  3,  4. 
2,4. 
8,  4,  3. 


382 


APPENDIX. 


SECTION  G. 

Apparatus  to  iUuBtrate  wave-motion.  —  The  most  efficient 

apparatus  for  this  purpose  that  we  have  seen  may  be  constructed  as 
follows.  Procure  forty  wooden  return-balls  (sold  at  toy  stores) ;  sus- 
pend them  by  strings  (better,  fine  wires)  about  1"  long,  as  in  Figure 
302,  and  about  7""  apart.     Connect  all  the  balls  horizontally  by  small 


Fig.  302. 


elastic  cord  (better,  small  spiral  wire  coil),  and  connect  the  ball  at  one 
extremity  of  the  series  with  a  suspended  weight  B  (weighing  about 
1  )  ,  and  from  the  ball  at  the  other  extremity  suspend  a  small  weight 
A,  which  may  be  easily  removed  when  desirable.  By  a  simple  vibra- 
tion given  with  the  hand  to  A,  a  wave,  as  CD,  will  be  projectec^ 
through  the  series,  and  on  reaching  B  will  be  reflected  ;  though  when 
reflection  is  wanted,  B  had  better  be  replaced  by  a  hook  attached  to  a 

WftUa 


APfJBINDIX. 


883 


most  eflBcient 
onstructed  as 
stores) ;  siis- 
as  in  Figure 
;ally  by  small 


e  ball  at  one 
ghing  about 
iinall  weight 
imple  vibrar 
be  projected 
hough  when 
ttached  to  a 


SECTION  H. 

Porte  Lumi^re.- Two  half-sections  of  a  tube  A  and  B  (Fig  303) 
may  easily  bo  sawn  from  a  block  of  pine  wood.     These  glued  togeth 
at  their  edges  make  the  tube  C.  together 


Fig.  303. 


This  tube  is  QO^m  long  and  IG"™  in 
diameter,  with  a  boro  of  l^"  diam- 
eter. Raise  a  window-sash  about 
50™,  and  fit  a  board  I)  just  to  fill 
the  opening.  In  the  middle  of  this 
board  cut  a  liole  just  large  enough 
to  receive  the  tube,  and  allow  it  to 
turn  in  the  hole  freely.  Attach  a 
bolt  E  to  the  board  D,  and  about 
12<"»  from  one  end  of  the  tube  bore 
a  row  of  holes  around  the  tube, 
I*""  in  depth  and  about  Ic™  apart' 
to  receive  the  bolt.    Uy  means  of  a 

aS:rttir7 

tacks  with  ia.ge  r...^^  !::'!jz:^:T^zt'7ii::^ 

^eXa^f  J;  "",  f  "^:  .^"^  '''^'  ^'  *^«  ^-d  -  -rtd  through 
the  tube  and  fastened  to  a  binding  screw  H.    When  the  mirror  is  to 

b    adjusted  so  as  to  receive  the  sun's  rays  and  reflect  them  through  the 

tube,  rotate  the  tube,  and  raise  or  depress  the  mirror  by  means  of  the 

heavens   and  then  fasten  by  means  of  the  bolt  and  string.     A  win- 
dow on  the  soutk  side  of  a  building  should  be  selected  for  elperfmrnts 
wiii  this  apparatus     The  portion  of  the  window  not  occupierwU 
the  board  I),  as  well  as  other  windows  not  in  use,  may  be  darke^ie 

Tnllf  ?  ''"'  """"^"'^'^  •^^^'h-     The  whole'  cost'  of  tL  above 
apparatus  need  iiot  exceed  «1.00. 


384 


APPENDIX. 


SECTION  I. 

ro^!fr.«i^''°!,  ?f  "^   ^^'^^*  '^^^^^   ^°^  Cotton   and  Silk 
AZr„^2t   ^tT    ""^.^^^^    Wire. -By   Browne  .   Sh^  e^ 
Ann  ncan  Gauge.     The  resistances  are  calculated  for  pure  copper  wire 
rhc3  number  of  feet  to  the  pound  is  only  approximate  for' h^suS 


No 


8 
9 
10 
11 
12 
13 
14 
15 
16 
17 

18 

19 

20 

21 

22 

23 

24 

25 

26 

27 

28 

29 

30 

31 

32 

33 
34 
35 
36 


i 

5 


.12849 
.11443 
.1018D 
.09074 
.08081 
.07196 
.06408 
.05707 
.05082 
.04525 
.0403 
.03539 
.03196 
.02846 
.02535 
.02257 
,0201 
.0173 
.01594 
01419 
.01264 
.01126 
.01002 
.00893 
.00795 
.00708 
.0063 
.00561 
.005 


Feet  per  Pound. 


Cotton 
Covered. 


42 
55 
68 
87 
110 
140 
175 
220 
280 
360 
450 
560 
715 
910 
1165 
1445 
1810 
2280 
2805 
3605 
4535 


Silk 
Covered. 


46 
60 
75 
95 
120 
150 
190 
240 
305 
390 
490 
615 
775 
990 
1265 
1570 
1970 
2480 
3050 
3920 
4930 
6200 
7830 
9830 
12420 


Naked; 


20 
25 
32 
40 
50 
64 
80 
101 
128 
161 
203 
256 
324 
408 
514 
649 
818 
1030 
1300 
1640 
2070 
2617 
3287 
4144 
5227 
6590 
8330 
10460 
13210 


Resistance  Naked  Coppeu. 


OhraB  Per 
1,000  Feet. 


.6259 
.7892 
.8441 
1.254 
1.580 
1.995 
2.504 
3.172 
4.001 
5.04 
6.36 
8.25 
10.12 
12.76 
16.25 
20.30 
25.60 
32.2 
40.7 
51.3 
64.8 
81.6 
103 
130 
164 
206 
260 
32S 
414 


Ohms     Feet  Per 
Per  Mile.      Ohm. 


3.3 
4.1 
4.4 
6.4 
8.3 
10.4 
13.2 
16.7 
23. 
26. 
33. 
43. 
53. 
68. 
85. 
108. 
135. 
170. 
214. 
270. 
343. 
432. 
538. 
685. 
865. 
1033. 
1389. 
1820. 
2200. 


1600. 
1272 
1185. 
798 
633. 
504. 
400 
316. 
230 
198 
157. 
121. 
99 
76  5 
61.8 
48.9 
39  0 
31.0 
24.6 
19..'; 
15.4 
12.2 
9.8 
7.7 
6.1 
4.9 
3.8 
2.9  i 
2.4 


Ohms  Per 
Pound. 


■  0125 
.0197 
0270 
.0.501 
079 
.127 
.200 
.320 
513 
.811 
1.29 
2.11 
3.27 
5.20 
8.35 
13.3 
20.9 
33  2 
52.9 
84  2 
134. 
213 
338. 
539. 
856 
1357. 
2166. 
3521. 
5469. 


and  Silk 
Ss  Sharpe's 
)pper  wire. 
*  insulated 


PPER. 

Ohms  Per 

round. 

-012.) 

.01!»7 

0270 

.0501 

07!) 

.127 

.200 

.320 

513 

.811 

1.29 

2.11 

3.27 

5.20 

8.35 

13.3 

20.9 

33  2 

52.9 

84  2 

134. 

213 

338. 

539. 

856 

357. 

106. 

521. 

409. 

IKDEX. 


[The   Numbers   repeb  to   Pages.] 


CHAPTER  I, 


Absorption  of  gases  by  solids,  41. 

of  gases  by  liquids,  42. 
Ailhegiou,  ^G. 
Aiiiorplious  bodies,  28. 
Attraction,  Mutual,  16. 

Phenomena  of,  23. 

Brlttlenegg,  34. 

Capillarity,  37-39. 

Laws  of,  39. 
Chance,  Absence  of,  2. 
Changes,  Physical  and  chemical,  12. 

of  volume  by  crystallization,  29. 
Cleaveage,  Plane  of,  27,  31. 
Cohesion,  26. 

in  water,  21. 
Colloids,  44. 
Crystallization,  27. 

Change  of  volume  by,  29. 

Cause  of  tendency  to,  30. 

of  water,  28. 

of  iron,  30. 
Crystalloids,  44. 

Density,  11. 
nialysls,  44. 

Dimiston  of  liquids,  42. 

through  porous  partitions,  43,  4.5. 

of  gases,  44. 

fountain,  40. 
Ductility,  35. 

Slastirity,  32, 

Perfect,  34. 

Limit  of,  34. 
Endosmose,  43. 
Exosnnose,  43. 
Kxperlmentatlon,  3,  4, 


Flexibility,  32. 
Fluidity,  35. 
Force,  15. 

defined,  16. 

Molar  and  molecular,  16, 18. 

of  gravity,  17,  24. 

Gases,  Distinguishing  property  of,  20. 
Gravitation,  23. 

Hardness,  31. 

Scale  of,  32. 
Heat,  0. 

Effect  of,  on  solution,  40. 

Impenetrability,  4,  9. 

I'lqulds,   Distinguishing  properties 
of,  19. 
Incompressibility  of,  21. 

JRIalleablllty,  35. 

Mass,  11,  23. 

distinguished  from  weight,  25. 
Matter,  3. 

An  essential  property  of,  4. 
Compressibility  of,  17. 
Constitution  of,  9. 
Const^mt  quantity  of,  13. 
Crystalline  and  amorphous,  27. 
,  Minuteness  of  particles  of  6. 

Three  states  of,  18-22. 
Molecule,  7,  8,  9. 

IVature,  Order  of,  2. 

Absence  of  chance  in,  2. 

Law  of,  2. 

Law  of,  not  a  cause,  2. 

Means  of  obtaining  a  knowledge  of,  1. 

Osmose,  43. 


386 


INDEX. 


Phenomenon,  3,  4. 
Poreg,  Physical,  10. 
Porosity,  10. 

Repulsion,  Mutual,  16. 

Sensations,  1. 

and  Inferences,  2. 

and  things,  3. 
Senses,  1. 
Solids,  Distinguishing  property  of,  19. 

Limit  of  elasticity  of,  34. 

Solution  of,  40. 

When  wet  by  liquids,  37. 
Solution  of  solids,  40. 


Spring  balance,  33. 
Strain,  34. 

Stress,  34. 

Substanoe,  Simple  and  compound,  U, 

Tenacity,  35. 

Vp  anil  down,  25. 

Viscosity,  34. 

Weight,  23,  2ft. 

distinguished  from  mass.  25. 
Ueldlng,  27. 


CHAPTER   II. 


it  .1 


Action,  128. 
Alr-Pump,  57, 

Apparatus  for  raising  liquids,  77,  78. 
Atmosphere,  a  unit  of  pressure,  52. 

Pressure  of,  52,  57. 

Hight  of,  54. 
Artesian  wells,  73. 

Barometer,  53. 

Boyle*s  law,  62. 

Buoyant  force  of  fluids,  79-82. 

Center  of  gravity,  104. 

To  find,  106. 
Center  of  inertia,  105. 
Centrifugal  force,  109. 
Centripetal  force,  110. 
Condenser,  63. 
Couple,  Mechanical,  103. 

Density,  82. 
Direction,  Line  of,  105. 
Dynamics  defined,  47. 

of  fluids,  47. 
Byne,  137, 140. 

Energy,  131-133. 

contrasted  with  momentum,  136. 

Fnrn-.uUifor,  135. 
Potential  and  kinetic,  133,  134. 
Transformation  of,  140. 
Unit  of,  137, 140. 


Xiqulllbrium,  47. 

Three  atixUm  of,  106. 
Stable,  107. 
Neutral,  107. 
Unstable,  107. 

of  forces  acting  in  one  plane,  151-156 
Erg,  138,  140. 
Expansibility  of  gases,  56. 

Ealllng  bodies,  112,  114. 

in  a  vacuum,  115. 
Foot-pound,  132. 
Force,  Absolute  unit  of,  137, 140. 

Centrifugal,  109. 

Centripetal,  110. 

Component*  of,  94. 

Equillbrant,  103. 

Gravity  unit  of,  137, 

Measure  of  a,  135. 

Measure  of  the  effect  of  a,  138. 

Uesolved  part  of,  95,  97. 

Moment  of,  150. 
Forces,  Composition  of,  94,  98,  102. 

Graphic  representation  of,  93. 

Resolution  cJf,  95. 

Resultant  of,  94. 

Oases,  Compressibility  and  expanslbilltv 

of,  65.  ' 

Law  of  volume  and  pressure,  62. 


O 
P 


INDEX. 


387 


iinU  compound,  1 1 , 


Tiaas,  25. 


le  plane,  151-156. 
a,  55. 


137,  140. 


f  II,  138. 


84,  98,  102. 
I  of,  93. 


d  expansibility 
!B8ure,  62. 


Gravity,  Cent<'r  of,  104. 
To  find  center  of,  106. 
Acceleration  due  to,  114. 
Specific,  83-85. 

Horse-power,  13.'?. 
Hydrometer,  86. 

Hydrostatic  hcllowH,  07. 
presB,  67. 

Inertia,  83. 

Center  of,  105. 
Inclined  plane,  149. 

Klloj^rammeter,  132. 
Kinetic  energy,  133. 

I.iqul'i  surface  level,  72. 

Machines,  Uses  of,  143. 

Internal  work  done  by,  145. 
Law  of,  144. 

Efficiency  or  modulus  of,  145. 
^lechanical  units,  Summary  of,  140. 
Mariotte's  law,  60,  62. 
Moment  of  a  force,  150. 

Vanishing  of  moments,  1,50. 
Momentum,  126. 

contrasted  with  energy,  iS!y. 
Unit  of,  128. 
Motion,  89. 

All  matter  in,  89. 

arises  from  mutual  action  between  at 

least  two  bodies,  91. 
Accelerated  and  retarded,  90,  112, 115. 
Curvilinear,  109. 
Formulas  for  accelerated  and  retarded 

114,  115. 
First  law  of,  90,  92. 
received  by  masses  of  matter  gradu- 
ally, 91. 
Second  law  of,  93, 127. 
Third  law  of,  128, 129. 
Uniform  and  varied,  90. 
versus  rest,  89. 


OscUlaUon,  Center  of,  122. 
Parabolleoarve,  118. 


Parallel  forces,  Composition  of,  102. 
Pendulum,  121. 

Center  of  oscillation,  122. 
Center  of  percussion,  124. 
Compound,  122, 123. 
Useful  applications  of,  125. 
Time  of  vibration  of,  121,  122. 
Physics  defined,  141. 
Potential  energy,  1,33. 
Press,  Hydrostatic,  67. 
Pressure,  47. 

in  fluids,  48,  60,  51. 
Transmission  of,  in  fluids,  M,  67. 
in  fluids  due  to  gravity,  68-71. 
Projectiles,  117. 

acted  upon  by  two  forces,  117. 
Horizontal  and   vertical  motions  of. 

119. 
Examples  worked  out,  120. 
Path  of,  118. 

Range  or  random  of,  117. 
Pump,  Air,  57. 
Force,  78. 
Lifting,  77,  78. 

Random  of  projectiles,  117. 

Reaction,  128. 

Reflection,  Angle  of,  1.30. 

Law  of,  130. 
Resolved  part  of  a  force,  95,  97. 
Rest,  89. 

Resolution  of  forces,  93. 
Resultant  of  two  or  more  forces,  94. 


Screw,  149. 
Siphon,  75,  76. 
Speclflc  gravity,  83-85. 
Stability  of  bodi-  ,  107. 
Summary    of   mechanical 
formulas,  140. 


units    and 


Tension,  47. 

Torricellian  vacuum,  53. 
Tifauiifonnattou  of  energy,  140. 

ITnlta,  Summary  of  mechanical,  14C. 
I  GraviUtion  and  absolute,  137, 188. 


888 


tNDE.^. 


Vai'iiuiM,  Almoliiff,  50. 

'I'oriim.llliKi,  wi. 

KiillliiU  ImkIIi.h  \n,  116. 
VtslovMy,  \m. 

tli'lllli'il,  IH), 

UjiU  of,  140, 


H«;iKht  losg  at  equator  than  at  poles. 
110.  * 

Wheel  and  axle,  148. 
^Vork,  lol. 

Uate  of  doing,  132. 

Unit  of,  132,  140. 


CHAPTER  rri. 


Koillnif,  r.iitvN  „f,  182. 
Ii"l)it,  1(11. 

Coiiiliietioii  of  Jioat,  162. 

Coiiv«<!|| ,t  Uma,  las. 

CajmcUy  for  Ik'hI,  192. 

<'""•"'"  "f  illffort-tico  in,  193. 
Cold,  MuthodH  of  iirodiiclnK,  188. 
CoiiaerviiUoii  of  Mu-r^y,  Kta. 
Coi-rulMtlon  of  cncrKy,  1«6. 

Bew  point,  IHft, 
IMflrUiilon  of  iKMit,  101. 
DUUUatloii,  IHM. 

isotcu  of  Jioiit,  ins. 
i:uerfgy,  Conservation  of,  196. 

Corr«l«tlo«  of,  ]95, 
Kvaiioratlon,  184. 
li^ximiiiloii  liy  »i<mt,  188. 

Abuorinaj,  170, 

('oomclfiit  of,  109, 

Power  of,  170. 

Vreeztug  point,  171, 
Funloii,  l.iiwuof,  182. 
iinHtsa,  Kliuald  theory  of,  178. 

Diffusion  of,  179. 

I.awK  of,  177. 

PreHNuru  of,  179. 
Heat,  Ifl7-2<X). 

Capiiclty  for,  192. 

CondiKftlon  of,  102. 

Oonvo<!tlon  of,  io;i, 

couvL-rtlblo  Into  mochanical    motion 
157. 

dertnml,  lf,U, 
DiSlWlOtt  0/,  101. 


Heat,  Kffects  of,  168. 
Expansion  liy,  168. 
generated  by  chemical  action,  159. 
Latent,  187,  188. 
Liquefaction  by,  180. 
Mechanical  equivalent  of,  196. 
Origin  of  animal,  ]o<». 
Quantity  of,  161. 
.''udiation  of,  165. 
ic.ated  to  worl<,  158. 
Specific,  191,  192,  19.3. 
Thermometry,  171. 
Units  of,  185. 

Jonle'8  equivalent,  19«. 

Latent  heat,  187,188. 
l.aw,  Mariotte's,  177. 

of  Charles,  177. 
IiaM-8,  r'  fusion  and  boiling,  182. 

of  gaaeous  bodies,  177,  179. 
X,lquefactlon,  180. 

Table  of  melting  poinU,  182. 
I^ocomottve,  199. 

AIariotte'8  law,  177. 
itiechaiilcal  equivalent  of  heat,  196. 

Quantity  of  heat,  161. 

Radiation  of  heat,  105. 

Speclllc  heat,  191. 

defined,  192. 

Tabic  of,  193. 
Sun  as  a  source  of  energy,  360. 
Steam-enj^ine,  lyo. 
.    Condensing  and  uon-c  ...dengiug,  198. 


INDEX. 


889 


Temperature,  AbnoIiiUi,  1T«, 
deflned,  100. 

dlHtlii(fuished  from  (fuikaHty  t)(  hmt. 
161.  • 

meaaured  by  expi»n»loD,  171, 

MfUHurcmuiit  of  ttxtruinit,  17ft. 

ytunduid  UMiipc-rutiiritit,  171, 
Thcrino-nynaialea,  Klft. 
Thfrinometer,  171. 

Air.  174. 

Coimtnirtlon  of,  172, 


Thermometer,  Conversion    from   one 
BCJilo  to  another,  173, 
(iriiduatloii  of  171. 

Vaporization,  180. 

Uolllng  pointe  of  water,  182,  183. 
Ventilation,  105. 

Experiments  illuatratl.iK,  106. 

Bent  means  of,  16'( . 

Amount  required,  168. 


CHAPTER  IV. 


Absolute  units,  228. 
Accumulators,  298. 
Alpliabet,  Telegraphic,  29a, 
Ampere,  a  unit  of  current,  i',, 
Anp^re'8  rule,  204. 

theory,  240. 
Ampirlau  currents,  241. 
Armature,  218. 

Attractions  and  repulHlonn,  237,2(11,277, 
Aurora  tube,  279. 

Battery,  Electric,  203. 

Amalgamation  of  zinc  in,  20»i, 
Appearance  of  hydrogen  nt  the  mp. 

per  plate,  206. 
Arrangement  of  cellii,  22'.», 
Bunsen'g,  210. 

General  conciuBlonu  concurnliiK,  2.12, 

Gravity,  212. 

Gremt,  210. 

Grove's,  210. 

Smee's,  209. 

Local  action  In,  208, 

Perfect,  332. 

Poles  or  electrodes  of,  204, 

Storage,  298, 

Thermo,  258, 

Coll,  Ruhmkorfl's,  256, 

Induction,  255. 
Condenser,  274, 
Coulomb,  227. 


Current,  Electric,  202. 
Amperian  currents  241. 
Attraction  and  repulsion  between  cur- 
rents, 237. 
capable  of  doing  work,  214. 
Direction  of,  203. 
Extra,  254. 

First  law  of  currents,  2.37. 
malntjiined  by  chemical  action,  206. 
Ohm's  law,  220. 
Hecond  law  of  currents,  239, 
Strength  of,  218,  222. 
Unit  of,  227. 

Dlamagnetlsm,  247. 

nynamo  machines,  249. 
Commutator  of,  249. 

Karth  a  magnet,  242, 

Cause,  245. 

Mrgnetic  poles  of,  244. 
Electric  candle,  286, 

lamp,  286. 

motors,  289. 

light,  285. 
Electrical  attractions,  etc.,  237,  261,  277. 

machines,  249,  208,  270,  271,  281. 

measurements,  218,  221,  227,  228. 

resistance,  223, 224,  289. 
Electricity,  Chemical  effects  of,  213. 

Bound,  270. 
Current,  200. 


390 


INDEX. 


Kloctrloltjr,  Electro.motlve  force,  226 
Frictlonal,  260. 
Heating  effecta  of,  212. 
Lnmlnoiig  effect  of,  213. 
Magnetic  effect  of,  217. 
Physiological  effect  of,  216. 
Thermo,  257. 
Static  and  dynamic,  262. 
may  receive  and  Impart  energy,  282. 
What  is,  282.  BJ'.-'-'^- 

Blectrlflcation,  260. 

on  external  surface,  267. 

Two  kinds  of,  264. 
Blectro-chemical  series,  207. 
Electrodes,  204. 
£lectrolyg|g,  213. 

Electro-magnet,  217. 

Power  of,  233.  ' 

Electro-magnetic  machines,  249. 
J^lectro-motf  ve  force,  225,  281. 

of  induced  current*,  254. 
Slectrophorus,  269,  270. 
Electroplating,  288. 
Electroscope,  260. 
Electrotyping,  287. 
Knergy,  Electric,  How,  originates,  205. 

1  ransformatlon  of,  282. 

Examples,  28;j. 

Eire-alarm,  Electric,  293.       ' 

Galvanometer,  219,  220. 
Galvanoscope,  206. 
Teissier's  tubes,  279. 

Helix,  218. 

Induction,  Current,  263. 

colls,  256. 

Magnetic,  236. 
Insulation,  266. 

Effect  of  moisture  on,  266. 

l«eyden  Jar,  275. 
lieyden  battery,  276. 
I<''ghtnlng,  280. 
«>ds,  280. 


Magnets  and  magnellsm,  234,  247. 
General  remarks  on,  246. 
Compound.  247. 
Law  of,  236 

not  sources  of  energy,  247. 
Natural,  245. 

Permanent  and  temporary,  284. 
I'olarity  of,  2;J6. 
Magnetic  transparency,  238. 
Magnetic  needle,  Ampere's'nile,  204. 
Declination  of,  244. 
Dip  of,  242. 

Line  of  no  variation  of,  246. 
Magneto  machines,  249. 
Measurements,  Electrical,  218. 
Experiment*  In,  221. 
Summary  of,  227,  228. 
Units  of,  228. 
Microphone,  297. 

Olim,  228. 
Ohm's  law,  226. 

Paramagnetism,  247. 
Potential,  Electric,  204,  267. 
Points,  Effect  of,  277,  278. 


Helay  and  repeater,  290,  291. 
Resistance,  Formula  for,  228. 

Internal,  224. 

of  the  earth,  289. 

Table  of,  224. 


Storage  battery,  298. 

Telegraph,  289. 

alphabet,  292. 

sounder,  290. 

Facsimile,  292. 

Fire-alarm,  293. 
Telephone,  294. 
Thermopile,  288. 

Volt,  228. 
Voltaic  arc.  286, 
Voltameter,  219. 


I«ra,  234,  247. 
1,246. 


XJ,  247. 

porai-y,  2.S4. 

y,  235. 

pere's  rule,  204. 


of,  245. 

9. 

irical,  218. 

i. 


INDEX. 


CHAPTER  V. 


891 


r,  267. 

'8. 


IVolae  dlittngiilahed  from  musical  sound, 

315. 

Scale,  LIniltH  of,  317. 
Siren,  310. 
Sounds  290. 

Analysig  of,  32U. 

deflned,  308. 

How,  origlniitcH,  306. 

IIow,  travelM,  306. 

LoudncHH  of,  313. 

Media  of,  308. 

Pitch  of,  316. 

Quality  of,  319. 

Ueflectlon  of,  211. 

Refraction  of,  312. 

Velocity  of,  309. 

Wave-Boundg,  305. 
Spcakiiig-tulu'H,  314. 

Vacuum,  Sound"  cannot  travel  through 
a,  306. 


Velocltjr  of  sound,  .109. 

deiiends  on  density  and  elasticity  of 

medium,  309. 
Vibration,  dcHned,  :uM). 

Direction  of,  3(H). 

Loni^tudlual,  300,  306. 

Propaifatlon  of,  301. 

Simple  and  complex,  300. 

ToiHlonal,  300,  306. 

TrannverHe,  300. 

of  strings,  318. 

Wavefi,  Air,  .307. 
Amplitude  of,  301. 
Air  as  a  medium  of,  303. 
How,  propagated,  304. 
Length  of,  301. 
Longitudinal,  302,  ;503. 
Keflectlon  of,  301. 
transmitted  in  elastic  medium,  308. 
Transverse,  303. 
Water,  302. 


291. 
r,228. 


CHAPTER    VI. 


Aberration,  Chromatic,  369. 
Achromatic  lens,  370. 
Analysig  of  light,  356. 
Athermancy,  363. 

Beam  of  light,  323. 

Camera  obscura,  367. 

Photographer's,  367. 
Candle-power,  331. 
Color,  361. 

by  absorption,  361. 

Cause  of,  359,  362. 

Dew,  366. 
Diatliermancy,  363. 

Dlaperalon  of  light,  357,  359. 

Energy,  Padiant,  321. 
£ther,  a  medium  of  motion,  322. 


Gxclianges,  Theory  of,  365. 
Eye,  Human,  368. 

Foci,  Conjugate,  3W,  353. 
Focus,  Principal,  352. 
Virtual,  3.">3. 

Heat  and  chemical  spectra,  360. 
All  bodies  radiate  heat,  365. 

Images,  325. 

Formation  of,  341,  343,  344,  353. 
Real,  342. 
Size  of,  354. 

To  construct,  354. 
Virtual,  355. 

Hicnses,  3o0. 
Effects  of,  351. 


892 


INDEX. 


Iilght,  a  form  of  energy,  321. 

AnalyBis  of,  S.W. 

Diffused,  ;«7. 

Reflection  of,  3.36. 

Syntheses  of,  358, 
1-uml.ious  and  ill.nninated  bodies,  326. 

MJcroscope,  Simpk.,  35.-.. 

Compound,  366. 
Mirrors,  Reflection  from,  .338. 

General  effect  of  concave,  341. 

Opacity,  325. 

Pencil  of  light,  323. 
Penumbra,  328,  329. 
Photometry,  330,  3.31. 
Prisms,  Optical,  350. 

Radiation,  Only  one  kind  of,  361. 

Thermal  effects  of,  .363. 
Radiators,  Good,  365. 
Radiometer,  321. 
Ray  of  light,  323. 


J(-' 


Reflection,  336. 

from  concave  mirrors,  339. 
Refraction,  345. 

Cause  of,  346. 

Inde.v  of,  347. 

I-.aw  of,  348. 

Table  of  Indices  of,  348. 

Seeing  an  object,  324,  332. 
Sliadotvs,  328. 

Siie,  Methods  of  estimating,  333.  334 
Spectrum,  357. 
Stereoptlcon,  370. 

Telescope,  Astronomical,  367. 
Transluce>  oy,  395. 
Transparency,  325. 


TJmbra,  328,  329. 
Vndulatory  theory,  323. 

Velocity  of  light,  334,  335. 
Visual  angle,  332. 


ill 


TEST  QUESTIOJ^S. 


law;^^nrure;\ta^^^^^^^^  (D  an  observed  fact;  (2)  a 

2.-Classify,  under  the  foregoing  headings,  the  following  statements  :— 
^     (1)  The  volume  of  a  given  body  of  gas,  if  the  temperature  is  constant, 
vanes  inversely  as  the  pressure.  ^""^i-aiiu, 

(2)  If  the  temperature  of  a  litre  of  air  at  OT.  is  raised  to  TC.  while  the 

pressure  remams  constant,  the  volume  is  increased  to  ?,^  of  a  litre. 

(3)  The  temperature  of  a  substance  depends  upon  the  average  kinetic 

energy  of  each  molecule.  g  cui. 

(4)  If  the  E.  M.  F  remains  constant,  the  strength  of  an  electric  current 

varies  inversely  as  the  resistance  of  the  whole  circuit. 

^^^  te^nrTratirrl  P'"^'^"'"^'  *^^  ^°^""^  °^  ^  S^^  varies  as  the  absolute 

(6)  That  which  we  call  heat  is  molecular  kinetic  energy. 

(7)  If  a  litre  of  air  measured  under  a  pressure  of  one  atmosphere  is  sub- 

jected to  a  pressure  of  two  atmospheres,  while  the  temperature 
remams  constant,  the  volume  is  recfiiced  one  half  litre.  ^'"'P^''*'"'^ 

(8)  Equal  volumes  of  any  two  gases  at  the  same  pressure  and  tempera- 

ture contain  the  same  number  of  molecules. 

^^^  ^ct%hl^!Z'^  ""^^f  ^\  P',''  !?"^'^  ^"''^  *«  communicated  to  any  part 
tUrl^i  °^  a  fluid  the  pressure  at  all  points  in  the  fluid  is 

thereby  increasea  by  ;j  lbs.  per  square  inch. 

mt7Jir^Lff£T  *  wu  ^.'  ^^*^^  ''^'".^  suspended  for  a  year,  became  per- 
possess  1^  stretched.     What  property  does  this  phenomenon  show  gla«s^  to 

tht'^hl'f.'^rtl:^^  °"°  ^""l"*^  ^  '""P^  '»  ^'^  hands,  and  another  man  pulls 
the  other  end  of  the  rope  with  a  force  of  90  lbs.  What  force  does  the  latS 
compel  the  former  to  exert  in  order  to  retain  the  rope  in  his  hands  ? 

lOo'lh?"^  w"h!^  f  l^^^^f^  extremities  of  a  rope  pull  each  with  a  force  of 
lOOJbs.     What  IS  the  force  exerted  between  them,  or  the  tension  of  the 

from'wMch'theTirl^!?''*""^  *.^  '?^'^t^  ^  P^'"«*^  Magdeburg  hemispheres 
Laches  ?  ^"^''^^y  exhausted,  and  whose  diameter  is  five 

a  Jkle^wS!  r°"^'^  be  necessary  to  separate  the  above  hemispheres  at 
a  place  where  the  barometrical  column  is  20  inches  ?  f       »  *«< 


394 


TEST  QUESTIONS. 


11 


Si 


lis  aLiLiii 


force  of  gravity  acting  on  each  ?  ^'         ^'  ^^®''*  '«  produced  by  the 

effel-'Vrtfty  wifl^Xf  ^"'  *'^  ^*"°^  ''«  ™*'  -•-*  changes  in  the 

in  ia^rh^e?  tt  hTgSf  vS  LTat^S^t  ?,\f  ^  ^  JJe  rubber  pressed 
air  increases  as  the  vessel  is  raised  ?         "  ^^"'^  **""  pressure^^of  the 

drJprte^fSte^^^^^  and  let  both 

simultaneously,  the  boarLeachesXroundlrft/Txplain  '"'  '^"PP^'^ 

Btop'unSuM^^^^^^^  of  the  cylinder  .  and 

applied  to  the  piston  to  Dull  it^f«  tL  i!  ^7^'"^e'-.  What  force  must  be 
the  transverse ?ectionStSpstonbe^fi2Scm,°^*''«  ^^linder,  the  area  o? 
at  the  beginning,  is  at  the  middirof  the^vlSZ  wK'%**'''*  *^"  P^^^o^' 
keep  It  in  motion  be  constant"  a kL,*u^^'^'  ^'^^  *h«  force  required  to 
reaches  the  bottonr:;S  tLVelv^'suppSr^^^  force^hen  i? 

drawn,  what  will  happen  ?  Suppose  tdnnn it  f  l^^^  P°^"'  '«  ^i«>- 
person  were  to  blow  with  a  forcfof  ?of  thp^frJf  f  i°  ^'  "^^^'•*«'''  ^"d  a 
bore  of  the  tube  being  iQcn^  Xt  we.Vht^^?  f  °^  the  cross  ser  J  ^on  to  the 
sustained  ?  If,  while  thus  in^Prtp/tL^  *  ^^^^"^  "P*'"  *•>«  P'^ton  might  be 
2m  above  the  lower  extrem^^roflhew'  "^^'\«'»'*y  of  the  tube  is  faised 
tube  until  it  is  filled  wWwp,v^f  1  ^i**'"'  ^""^  "^^t^"^ '"  Poured  into  the 
by  the  water  '  What  name  wSd  fc''^  "P°".'*^'  P'^'<^"  ^'"  be  susSined 
Suppose  thataplug   iustTttTncr  tHp?\*f?P*''*^l''^^«"'«  '°  the  last  case" 

the  tube  pressin^|S£7at?rr;ttTout\tlt^^^^^^ 
fourthTof  JhlTrtas  been're^r  *M  ^°  "V^  P"*"?  ^^'^^i^'' '«  20-.    Three- 

1.5.  What  ^t:^:::-:t^-:^t^^z  ^^-^  -^^« 

ra^'olirS^n  W  1?^?^%?*"^'  "'/'?  '«  '".?^^"^  <^-  «-*  -*  the 
order  that  his  resultant  'nTt;  ^*u  ™?^*  ^^  "^^^^  due  south-west  in 

southerly  veli^ifr^-^'^vrbr-oS  ^^hat  will  ^£ 

the'tileVaS  it's J:  rSfast^tre^ra?*  fl  ^^*,^  ''  ''  ""^  -  '--  ^ 
wind  carries  it  due  north'we8t2;th«^«t  ff  ^ '"' ^  ^"  ^"ur,  while  the 
its  actual  course  and  velocTtyl  °^  ^°"'  '"'*'"  ^"  ^«"'--     What  is 

Jh\-;ilXuU%1'tt^Van^^^^^  "^  ^^PV"'^  *-  -".  one  in 

At  wiiof  ..«•"*  ;f  -   !        *^  -     PO'°t  between  them  will  th""  •r—t  » 

—  I'^tiiu  ii  uuiy  one  m&n  puils  ?    Why »  "        "^       '^   ' 

18.-State  three  causes  for  the  variation  of  gravity  on  the  earth's  surface. 
19.-Can  you  move  without  the  aid  of  some  other  body? 


TEST  QUESTIONS. 


395 


B  hemispheres  at 
n? 

her  stone  of  the 
produced  by  the 

changes  in  the 

3  rubber  pressed 
3  pressure  of  the 

■d  and  let  both 
d  and  dropped 
in. 

cylinder  s,  and 
force  must  be 
der,  the  area  of 
ihat  the  piston, 
)rce  required  to 
B  force  when  it 
:  point  is  with- 
nverted,  and  a 
3  ser ;  'on  to  the 
iston  might  be 
!  tube  is  raised 
oured  into  the 
11  be  sustained 
the  last  case  ? 
re  forced  into 
IS  become  ? 

20cm.    Three 
iceiver  weighs 
plate  ? 

ue  east  at  the 
jouth-west  in 
t  will  be  his 


iles  an  hour  ; 
ir,  while  the 
ir.     What  is 

men,  one  in 
they  meet  ? 

th's  surface. 


20.— Bodies  at  rest,  with  respect  to  the  surface  of  the  earth,  are  really  in 
motion,  and  their  motion  is  not  constant  nor  in  a  straight  line.  Are  the 
forces  which  act  on  them  in  equilibrium  ? 

21.— Upon  which  will  the  eflfect  of  a  given  force  be  greater,  a  body 
initially  at  rest  or  a  body  in  motion  ? 

22. — Express  the  atmospheric  pressure  at  sea- level  in  absolute  units. 
23.— Why  are  "top-heavy  "  bodies  unstable  ? 

24. — What  mechanical  advantage  may  be  gained  in  a  copying  press  in 
which  the  hands  move  through  1  mch,  while  the  end  of  the  screw  descends 
tJ-j  inch  ? 

25. — How  many  cubic  feet  of  water  will  a  lO-horse-power  engine  raise  in 
an  hour  from  a  mine  300  feet  deep,  a  cubic  foot  of  water  weighing  62^  lbs? 

26. — When  a  force  acts  on  a  body  at  right  angles  to  the  direction  of  its 
motion,  so  as  to  cause  it  to  revolve  in  a  circle,  does  it  do  work  on  the  body? 
Why?  "' 

27. — Does  the  sun  do  work  on  the  planets,  which  revolve  about  it,  by 
virtue  of  the  mutual  attraction  between  it  and  them  ?    Explain. 

28.— Is  the  energy  of  the  planets  increased  by  this  attraction  ?  Do  the 
planets  move  in  circular  orbits  ? 

29.— When  a  force  acts  upon  a  body  and  causes  it  to  move  a  given  dis- 
tance, in  what  language  would  you  describe  the  effect  of  the  force  ? 

30. — How  does  energy  differ  from  power? 

31.— If  an  engine  should  raise  55  lbs.  10  ft.  in  a  second,  and  at  the  end  of 
a  second  its  energy  should  be  exhausted,  could  it  properly  be  called  a  one- 
horse-power  engine  ? 

32. — A  cannon  ball  is  shot  into  empty  space  ;  how  great  a  force  will  be 
required  to  deflect  it  from  its  path  ? 

33. — Can  a  child  sitting  on  a  sled  start  or  stop  the  sled  by  pulling  on  a 
cord  attached  to  the  sled  ?    Why  ? 

34. — Why  does  not  every  body  move  when  acted  on  by  force  ? 

35.— Why  does  a  body  thrown  horizontally  into  the  air  fall  to  the  earth  ? 

•  36. — Is  the  expression  "one-horse-power  per  second  "  admissible,  as,  for 
instance,  when  we  wish  to  convey  the  idea  that  a  horse-power  lasts,  or  is 
exerted  for  one  second  ? 

37. — How  many  dynes  of  force  are  required  to  set  a  mass  in  motion  ? 

38.— How  many  dynes  are  required  to  make  a  gram-mass  move  with  a 
velocity  of  9'81m  per  second,  the  force  acting  constantly  for  one  second  5 
What,  if  it  act  for  two  seconds  ? 

39. — What  is  the  force  acting  on  a  falling  gram-mass  in  Ontario? 

40. — Is  a  spring  balance  a  force  measurer  or  an  energy  measurer  ?  Why 
will  it  not  answer  both  purposes  ? 

41.— How  can  a  force  of  6  lbs.  raise  a  ton  10  ft.  with  a  perfect  machine! 


m 


J<  If 


I! 


"Iff! 

P 

I" !       ' 


i;i-- 


1 

li 

ill  'i 

:       ; 

1 !  '■ 

i 

fir 

TEST  QUESTIONS. 


42 — A  pebble  stone  weipJm  f..  n.v  oa,»     • 

^tlww  iir  '"T'  "«'"""  ^  -»'  ^»^^  --  a  COM  W,  . 

^«- *h™"p^^^^^^  in  flannels  in  the  sun^mer  ?    How 

peS-^e'-be  lowfe  °'  "^""^^  »~  -lorie  ,  how  much  will  the  tem 
,£-How  .any  .ilogra.s  of  ice  at  0=  C.  can  be  .elted  b,  .  of  stea.  at 

52;:rt::s^^^^^ 

waterfrom  0=  C.  VlPhT    *  '^^  ^^  ^^"^'^  ^^  '-^quired  to  raise  500k  of 

mettuTi^Sll^ee^T^ptntX^^^^^       .T  ^^^^*™  -'^  ^'ght.  and  on 
"If  *^r  «t  was  found  to  be  45  vdts      \VhT  *^'!u''^°  ^^^''^^^^  by  ai  elect  ° 
absorbed  by  this  lamp  ?  °'*'-     ^^^^<=  ^^^  the  amount  of  horse  poier" 

a  et7n?7S^4rslTSnS^^^^^^^^^^         -  ^-M-F.  of  60  volts  and 
horse^^wer.  the  loL  of  energylS  'i^^ZS:^'^^^^;^::^  l^X^ 

f  ^^  "?  ^*^^-:;S^- -  I^?  a^    -e.^^^  line 

they  be  c.  nnected  f  ""'"^  '"  ^'^^  ^"^^  'circuit,  by  which  method  shouTd 
^;[^i^^^l^l^ireator,,intai.  ^  current  of  20  amperes  in  a 
»?Sf ^iT ?;Ln^^t^--,5S r  '-  ^-  ^-  «^  ^  volts  fnmish 


EXAMINATION   PAPERS. 


397 


5r  It  weighs  15g  ; 
'ecific  gravity  of 
3?    What  18  the 

statement. 
n  when  an  open- 

i  body  ? 

Jmperature  of  a 
;o  expand  ?    In 

a  body  may  be 
e  heat  in  these 

immer  ?    How 

I  will  the  tern- 

l"^  of  steam  at 

3f  iceatO°C.? 
'  raise  SOOk  of 

igbt,  and,  on 
^y  an  electro- 
horse-power 

GO  volts  and 
ig  15  (useful) 
t.  ? 

II  furnish  a 
a  such  bells 

legraph  line 


xternal  re- 
n?  If  two 
hod  should 

ip^res  in  a 

ts  furnish 


( 


an^E'lTp^ofV'v^lJu*?'  resistance  of  a  circuit  in  which  a  battery  having 
aatij.  m.  tf.oi  2  volts  furnishes  a  current  of  0-5  ampere  ?  J'       vmg 

m^l'i^eT^*  ''  **""  "'°'*  convenient  test  of  the  E.  M.  F.  of  an  electrical 

nf +JT^^  *  sounding  body  moves,  how  will  its  motion  affect  the  wave-lencth 
?/ont  ?  5ow  ZiUfi  •*  '^.T'.  Ju'*^^"^  •     H«^  ^"1  i*  affect  thosHhrowK 

of  ttiSn"Ji;'bodf r"'" ''  p'*'''  '^  "^'^  "^^  °*  *°  ^^^°"^^*«  *^«  -1-ity 

65.— How  does  one  color  differ  from  another  color  ? 
thfoVh^'aroitTp^ffi"  *'*'  «^P^™*^-  °^  -1-s  when  white  light  parses 

Nam;";r'e'oliio?nif.?''f^  '1-'S°^  ''  ''"""^^^  mirror  on  a  beam  of  light: 
S!  P        °^  "P*'"'''^  apparatus  that  will  produce  the  same 

elong^KrilSi;r«"  ''  "  "«'' ^^  '''''  '''  ^**^^  --"^  -°"nously 

D^s  ^^mLa  r*oZ  oS  S Lt*/"  """  ^'"'^^  *"^^^  *°^^^^  *^«  «^^ ' 


EXAMIISrATIOlSr  PAPERS. 

EDUCATION  DEPARTMENT,  ONTARIO. 

MIDSUMMER  EXAMINATIONS,  1887. 

THIRD  CLASS  TEACHERS. 

4. — What  in  nnh<itiinn  '      uru-t    _  u    i^       ■ , 

were  no  cohe'rron  7  T* '„.  "  .u-  '''°"^'^  ^^  '^^^^  oondition  of  things  if  there 
what  then?        "^    "  ovorythmg  possessed  cohesion  to  a  greS  extent? 

hafjoSouT"'  °°"'^  y°"  ^^°^  ^'^^^  ^**^^  has  cohesion  ?  That  mercury 


398 


EXAMINATION  PAPEBS. 


5.-H0W  is  a  barometer  made  ?    Mention  the  uses  of  a  barometer 
specmS  0I  Sf  '^^*  •    ^^^^"''^  -  -P-iment  to  show  thl  great 
doLl?i;7  t'ef ""  ''  ""'•    ''"^  '^  ^«  ««*™-t«  the  amount  of  work 

oft;;^eT?s15iftr79rm^^^^^^ 

[Is  that  which  is  called  latent  heat  really  heS^  J    '"'^"^  ^^"^'  ^  ^ 
9— Show  the  course  of  a  ray  of  light 

(a)  through  a  flat,  thick  piece  of  gla^s  ; 

(6)  through  a  piece  of  glass  shaped  like  a  wedge 

intoVatSl-dX^^^^^^^^^  of  a  blow  is  changed 

of  dec-^m^oslngl^ateT  ^°"  "''"''  ^'""  *^^*  *  -°1^-  battery  has  the  power 


MIDSUMMER  EXAMINATIONS,  1887. 
SECOND  CLA  S  TEACHERS. 

^':l^rft^'rolZ^^^^^^  at  an  angle  of 

J^-StateNewton'sSecond Lawof  Motion,  and  show howitapplies  in  the 
(«U  Ull  thrown  vertically  upwards  from  the  hand  of  a  person  at 

^'IfotS,*'^""'^  ^^'^^^-^y  "P--ds  from  the  hand  of  a  person  in 
^  (C-)  a  body  projected  horizontally  from  the  top  of  a  cliff. 

drawn^uf  a":ith  pfcSit  iXn' S  atS1n:^/  T «^*  °^  ^«  ^^«-  >« 
the  horizon?  ®°^'^'*  *°"* 'helmed  at  an  angle  of  30"  to 

rwv,»r-'  ""^  -"--■!"-".'  tu  show  the  trutii  of  this  law. 


EXAMINATION   PAPERS. 


399 


barometer. 

'  show  the  great 

amount  of  work 

whose  height  is 
at  he  may  reach 

'■  the  latent  heat 
equal  to  ? 


»Iow  is  changed 
^  has  the  power 


at  an  angle  of 
applies  in  the 
of  a  person  at 
>f  a  person  in 


t  of  40  lbs.  is 
igle  of  30°  to 

the  relation 


■e  be  said  to 


6.— State,  with  reasons,  what  will  take  place  in  the  case  of 

(a)  a  siphon  in  action  under  the  receiver  of  an  air-pump  at  work ; 

(b)  a  barometer  under  the  receiver  of  an  air-pump  at  work  ; 

(c)  ajjarometer  in  a  closed  vessel  filled  with  air  to  which  heat  is  bemg 

,r2'~T^  body  floats,  partly  immersed,  in4)ure  water  which  exactly  fills  the 

dronld°?n^T.^''-  .A«r'h  salt  as  the  water  will  dissolve  is  ^carefully 
dropped  in.     State  minutely  what  will  take  place.  ^ 

If  the  body  had  been  floating  wholly  immersed  what  would  have  occurred? 

h.hJ'L^^'l^''}^*''  fV^Pi<^*'ng  t'»at  air  had  weight,  and  wishing  to  verify  his 
to  wP,Vh  /^^'"^  *  ' • '"u^re*  ^'"P^y  ^"'J  *^^"  '"Sated  with  air  ;ind  finding  i? 
WhllSi  I-  ^"^  ?°  H*'^  ^?'^^'  concluded  that  air  was  a  weightless  fluid." 
Why  did  his  experiment  fail  ?  * 

9. — Define  specific  gravity. 
o..hinf^'%^'^\°^  "^^^u  weighs  1  000  oz.,  find  the  apparent  weight  of  a 
iron  beS^  7  2T    """^  ""'^        '°  ''^^''  *^'  '^^^"^  ^^^^''^  °*  ''^^^ 

actton~d^pends.^  *^^  ''^^°°'  ^""^  *''^^^'°  "^^^^'^^  ^^^  principle  on  which  its 

«in?^rj?rP*v7T^^°^^J°°*'''^^!P^°'^*'  gravity  =-8)  can  be  emptied  by  a 
c?!^  be7ng'f3  5l  ^^'''''''^'  '^^'  **  30  inches,  the  specific  gravity  of  mer 

11.— State  Boyle's  Law. 

The  mercury  in  a  barometer  stands  at  30  in.,  and  the  sectional  area  of  the 
tube  18  one  square  inch.  A  cubic  inch  of  air  is  admitted  through  the  mercury 
intT  the  vacuum  above  and  depresses  the  column  of  mercury  through  three 
mches ;  find  the  size  of  the  vacuum.  '  ""'''"S"  """^ 


JUNE,  1887. 


SECOND  CLASS  PROFESSIONAL  EXAMINATIONS, 
NORMAL  SCHOOLS. 


Note.— 75  per  cent,  of  the  value  of  this  paper  counts  100  marks  — the 

maximum. 

ani'7o^!"*'°?u*°y  °  v**"^  ^"^^  w'"*^^  go^e^*^  tl^e  expansion  of  solids,  liquids 
and  gases  on  the  application  of  heat.  -"'luo,  niiuuis, 

«ho;rf'L*iV-^''K  ^"^^  Yi*^  '?°  ^'^^^''  '^  ^^^^^  o"  a  %varm  stove.  In  a 
Sterwrdsth.'w«r' W*''^*  the  water  does  not  fill  the  vessel,  but  soon 
^*lTi„    *^^  "^^^^  '^  ^°"°*i  *°  ^^  "-"""ing  over.     Explain  the  causes  in 

^   3. -Explain  why  it  is  that  some  kinds  of  food  cannot  be  cooked  by  boil- 
ing  in  an  open  vessel  on  the  top  of  a  high  mountain. 
[How  would  you  arrange  a  vessel  in  which  to  cook  them  by  boiling  ?] 


fM> 


400 


-^ 


EXAMINATION   PAPERS. 


posed  of  a  number  of  differently  colored  lights?  '  ^''^^  ''^'*"  ^^8^*  "  ««'»■ 
Wanfay  tt^S;'  "'^'=*'°'^  ^^  ^--^e  experiments  by  which  these 
W^  S^^F:Z^J^:i^^^^y>  -^  -P^^^'^  ^ts  mode  of  action. 


11  ' 

I     t     I 


MIDSUMMER  EXAMINATIONS,  1886. 
THIRD  CLASS  TEACHERS. 

of  water  and  the  ice,  or  the  steam,  Sto  whTcK?'*"!"""  "^  8'^^"  q«a°«ty 
^c^l^you  prove  this  in  -y  partic^r^ J^s^ 'I  ^hot  Xl^^^^^^^^^ 

ex|ti;e^tf UKS^^^  will  suffer  a  loss  of  weight 

waterv' *  ^'"  ^^PP-  'f  *h^  -bstance  be  lighter,  bulk  for  bulk    than 
What  practical  applications  are  made  of  the  fact  which  you  haJe  just 

water.     Boiling  water EureTonthe^o^^  ''■'"'^'^y  fi"ed  with 

mediate  y  the  ^ater  insidHhe  pi>  Ldns  to'lk*'''^r  T^  ^'"^°«*  "» 
After  a  time  (the  boiling  water  stSl  Sfnl         ^u'     ^^^  ^""^^  i*  do  so  ' 
the  p.pe.     Why  does  it  do  so  v  ^        "^  '^"^  ^^^  ^^'^^  begins  to  rise  in 

these  powers.  ^""ou  some  practical  applications  of  each  of 


S^^->^^^^^^^^^  the  famous  inventor,  Mr 

influence  which  iron  undeTgoes  a^L  t.mn  ^1'° '^"'^^P^^^'ty  to  maguet/c 

eectricenergyfromfuel  witK  the  nliS^^  is  c&anged,  to  produce 
his  contrivance  a  "Pvrouino-nAHn  n  '°'*^y,6°won  of  a  steam  engine  Hb  naUa 
crude  stete,  it.is  abS^a^^Slfif  t?"]:-^^.^!.^*^  at  prLrnt  in^'onlf: 

^i°I"l^?^^-^/"amo,  while  it  re"^urr'es"no  att.^^^r/ii°,e.?i  V.'«  «team  engfne 


Edison  read^a  P^er  on  to^^'nV^ffn  beL'el^^r  ^  *?  ^^  ^*  '^"X 
Advancement  of  Science  at  itslast  session  ^«ie"can  Association  i 


.     Mr. 
for  the 


g  a  beam  of  white 
vhite  light  is  com- 

its  by  which  these 

1  mode  of  action. 


liquid,  and  a,  gas? 
a  given  quantity 
inverted."  How 
ould  you  weigh 

a  loss  of  weight 
ibe  experiments 

for  bulk,  than 

you  have  just 

in  water  ?] 
otion  possesses 

motion  of  the 

fly  filled  with 
ud  almost  im- 
loes  it  do  so  ? 
Jgins  to  rise  in 

n  do."  State 
ns  of  each  of 


I  inventor,  Mr. 
ty  to  magnetic 
i,  to  produce 
ine.  He  calls 
sent  in  only  a 
steam  engine 
unning.  Mr. 
iation  for  the 


v> 


Or 


X 


<^:' 


ei' 


;-^- 


'^ 


■"..,' '  '"'Wf^^^w 


N  L  C   B  N  C 


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